How many 4 digit numbers can be formed using 5 only ones but 5 must be used in all such numbers?
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Hello. This lesson will cover a few examples to help you understand better the fundamental principles of counting. Example 1 Find the number of 3-digit numbers formed using the digits 3, 4, 8 and, 9, such that no digit is repeated. Solution The ‘task’ of forming a 3-digit number can be divided into three subtasks – filling the hundreds place, filling the tens place and
filling the units place – each of which must be performed to complete the task. Now there are 4 ways to complete the first subtask (i.e. filling the thousands place), since we have 4 digits to begin with. Next, there are 3 ways to complete to fill the tens place (the second subtask), as now there are only 3 digits left to be used (repetition of digits isn’t allowed). Lastly, there are 2 ways to complete the third task. Therefore the total number of ways to complete the
task (which equals the required number of 3-digit numbers) will be 4 x 3 x 2 = 24. Pretty neat. I’ll list out the 24 numbers, in case you don’t believe me: 348 349 384 389 394 398 438 439 483 489 493 498 834 839 843 849 893 894 934 938 943 948 983 984 Note that the digits could have been filled in any order, not necessarily in the order which I did. The answer obtained would have been the same. Example 2 How many 3-digit numbers can be formed using
the digits 4, 5 and 6, such that the digit can repeat? Solution This seems similar. But this time the number of ways to fill the hundreds, tens and the units place would be 3 in each case, (and not 3, 2, 1) because the digits are allowed to be repeated. Therefore the number of such 3-digit numbers would be 3 x 3 x 3 = 27. I’ll list them out again. 444 445 446 454 455 456 464 465 466 544 545 546 554 555 556 564 565 566 644 645 646 654 655 656 664 665 666 Okay. Let’s
move on to a little more complex problems. I’ll stick to counting numbers in this lesson. Example 3 Find the number of 5-digit even numbers formed using the digits 1 to 9, such that repetition of digits is (i) allowed (ii) not allowed Solution I suggest that you grab a pen / paper and try to compute the answer yourself before reading further. (i) In this case we have a restriction on filling the units place, as the number needs to
be even. There are only 4 ways to do so (using 2, 4, 6 or 8). For the other four places, we have 9 choices each (as repetition is allowed). Therefore the number of ways will be 9 x 9 x 9 x 9 x 4 = 32805 (I won’t list the numbers this time. You have no option but to believe me.) (ii) This one is a little tricky. You might say that the answer is 9 x 8 x 7 x 6 x 4, as there will be 4 ways to fill the last digit (using 2, 4, 6 or 8). But there’s a problem. We’re not sure that after filling the first four places (from the left), whether we’ll be left with 4 choices for the units place or not. Because one of the even digits might have already been used before we reach the units place. To get around this problem, we fill the units place first using the even digits, followed by 8, 7, 6 and 5 choices respectively for the remaining places. Therefore the number of such 5-digits numbers will be 4 x 8 x 7 x 6 x 5 = 6720. Example 4 Find the number of 4-digit odd numbers formed using the digits 0 to 9 such that repetition of digits is (i) allowed (ii) not allowed Solution The units digit in this case can be filled in 5 ways (using the odd digits). Now, there are only 9 ways to fill the thousands place, as 0 cannot be used there. The remaining places can be filled 10 ways each. Therefore the total numbers in this case would be 9 x 10 x 10 x 5 = 4500. (Note that this is half of the total 9000 4-digit numbers possible, the other half being even) (ii) We’ll first fill the units place with an odd digit – 5 ways. Next we have the thousands digit – 8 ways (leaving out the 0). Finally, 8 ways for the hundreds place (the 0 is back) and 7 ways for the tens place. The total number will be 5 x 8 x 8 x 7 = 2240 I guess that’ll be it for this lesson. As a practice problem try and count the number of 5-digit even numbers using the digits 0 to 9, with and without repetition. The next lesson will establish a few formulae / expressions to deal with specific situations. See you there! 5 digit numbers are the integers on the number line that start from 10,000 and go up to 99,999. These numbers contain a total of 5 digits in their numeric form. Let us learn more about numbers up to 5 digits in this page.
What are Numbers up to 5-Digits?Five-digit numbers start from ten thousand and extend up to ninety-nine thousand nine hundred and ninety-nine. These numbers contain integers at the places of ones, tens, hundreds, thousands, and ten thousands. Any positive integer can be placed at these places, keeping in mind that 0 cannot be placed on the ten thousands place. This is because if 0 is placed here it will become a 4-digit number, like, 04356 becomes 4356. The following figure shows how a random 5-digit number, 86953 is placed on an abacus. The place value of the five digits that make up the 5-digit number would be obtained by progressively multiplying the respective figure by 1, 10, 100, 1,000, and 10,000 starting from the rightmost digit and moving to the left. Smallest 5 Digit NumberThe smallest 5-digit number is 10,000 because 5-digit numbers start from 10,000 and the number before 10,000 is 9999 which is a 4-digit number. Greatest 5 Digit NumberThe greatest 5-digit number is 99,999 because the number after 99,999 is 1,00,000 which becomes a 6-digit number. Place Values of Digits in Numbers up to 5-DigitsAs shown above, in a 5-digit number, every progressive place value is the earlier place value multiplied by 10. For example, let us take a number: 37,159. This number can be represented in words, as, 'thirty-seven thousand one hundred and fifty-nine'. The following figure shows the place values of this 5-digit number.  How to Decompose 5-Digit Numbers?When we see a 5-digit number, the five digits will correspond to the 5 place values - Units, Tens, Hundreds, Thousands and Ten Thousands. Let us see how a 5-digit number can be decomposed into its place values. Let us continue with the same number 20340. 2 is in Ten Thousands place = 2 × 10000 = 20000. Here, 0 is in Thousands place = 0 × 1000 = 0, and 3 is in Hundreds place = 3 × 100 = 300, 4 is in Tens place = 4 × 10 = 40, and 0 is in Units place = 0 × 1 = 0. Hence, the five-digit number can be expressed in the following way: 20000 + 0 + 300 + 40 + 0 = 20340. Now, how would the 5 place values change if we interchanged some of the digits? Let us change the number 20,340 to another 5-digit number having the same numbers with interchanged digits, like, 32,004. The change in place value of the same 5 digits shows the following results:
In both the numbers given above, all the zero digits have zero place value. Commas in 5-Digit NumbersWe saw the use of commas in four-digit numbers, and the position of the comma is just before the digit on the hundreds place, that is, to the left of the hundreds place. In a 5-digit number too, only one comma is to be used, and it is to be placed to the left of the hundreds place. For example, the 5-digit numbers 32958 and 20340 can be better expressed as 32,958 and 20,340 which helps in reading the numbers correctly. How Many 5-Digit Numbers Can Be Formed?As we said earlier, 02340 is not a five-digit number but a four-digit number 2340. A five-digit number cannot have 0 as the first digit on the left, which is the ten thousand place. Overall, every one of the 5 places of a 5-digit number can be filled up in ten ways, because it can have 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So each of the five places can be similarly filled up in ten ways. Therefore, the total number of combinations possible are 10 × 10 × 10 × 10 × 10 = 1,00,000. Out of these 1,00,000 ways of forming a 5-digit number, we need to take out all the possibilities which have zero in the first position on the left (or the ten thousand place). When there is zero in the first place, the next position (Thousands) can be filled up in ten ways, as can the Hundreds, Tens, and Units places. So, the number of 5-digit numbers that have zero as the first digit are 10 × 10 × 10 × 10 = 10,000. If we subtract these 10,000 ways from the overall 1,00,000 ways, we are left with 90,000. Therefore, there are 90,000 unique 5-digit numbers possible. Important Notes on Numbers up to 5-DigitsHere is a list of some important notes related to numbers up to 5 digits. These are helpful while we solve questions related to this topic.
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FAQs on Numbers up to 5-DigitsWhat are 5-Digit Numbers?A 5-digit number is a number that has 5 digits, in which the first digit should be 1 or greater than 1 and the rest of the digits can be any number between 0-9. It starts from ten thousand (10,000) and goes up to ninety-nine thousand, nine hundred and ninety-nine (99,999). How Many 5-Digit Numbers are there?There are 90,000 five-digit numbers including the smallest five-digit number which is 10,000 and the largest five-digit number which is 99,999. How do you Read a 5-Digit Number?We read a 5 digit number from left to write, starting from the ten thousands place to the units place. For example, the number 21,356 is read from left to right, starting from 2, followed by 1, 3, 5, and then 6. In number names, it is read as twenty-one thousand, three hundred fifty-six. How do you Write 5-Digit Numbers in Words?We write the number name of a five-digit number just the way we read it. Starting from left to right, from the ten thousands place to the units place. For example, the number 31,279 is written as thirty-one thousand, two hundred seventy-nine. What is the Smallest 5-Digit Number?The smallest five-digit number is 10,000. It is read as ten thousand in number names. What is the Largest 5-Digit Number?The largest five-digit number is 99,999 and it is written as ninety-nine thousand, nine hundred ninety-nine, in words. What is the Sum of the Greatest and the Smallest 5-Digit Numbers?The greatest 5-digit number is 99,999 and the smallest 5-digit number is 10,000. Their sum is 99,999 + 10,000=1,09,999. Which is the Greatest 5 digit number which is a Perfect Square?The greatest 5 digit number which is a perfect square is 99856. This is the square of 316 which means 3162 = 99856. What is the Successor of the Greatest 5 Digit Number?The greatest 5 digit number is 99,999. The successor of 99,999 is 1,00,000 which is read as one lakh as per the Indian place value chart and is read as a hundred thousand (100,000) as per in International place value chart. How many four digit number which are divisible by 5 can be formed by using numbers 0 to 8 without repetition?Hence, total number of four digit numbers, without repetitions, which are divisible by 5 are 504+448=952.
How many 42 Answers By Expert Tutors
There are 9000 values and 2 out of 10 (or 1 out of 5) of them are divisible by 5, so 9000/5 = 1800 are divisible by 5 -- if repetition is allowed.
How many four digit numbers can make using 5 and 0?There are 8 four digit numbers form by using the digits 0 and 5.
How many 4Hence, there are 48 four digit even numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated.
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