How many different words each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants? Show
Given: Total number of vowels \[=\text{ }5\] Total number of consonants \[=\text{ }17\] Number of ways = (No. of ways of choosing 2 vowels from 5 vowels) × (No. of ways of choosing 3 consonants from 17 consonants) \[=\text{ }{{(}^{5}}{{C}_{2}})\text{ }\times \text{ }{{(}^{17}}{{C}_{3}})\] By using the formula, \[^{n}{{C}_{r}}~=\text{ }n!/r!\left( n\text{ }-\text{ }r \right)!\] \[=\text{ }10\text{ }\times \text{ }\left( 17\times 8\times 5 \right)\] Or, \[=\text{ }10\text{ }\times \text{ }680\] \[=\text{ }6800\] Now we need to find the no. of words that can be formed by \[2\]vowels and \[3\]consonants. The arrangement is similar to that of arranging n people in n places which are n! Ways to arrange. So, the total no. of words that can be formed is \[5!\] So, \[6800\text{ }\times \text{ }5!\text{ }=\text{ }6800\text{ }\times \text{ }\left( 5\times 4\times 3\times 2\times 1 \right)\] \[=\text{ }6800\text{ }\times \text{ }120\] \[=\text{ }816000\] ∴ The no. of words that can be formed containing \[2\]vowels and \[3\]consonants are \[816000\] Permutation is known as the process of organizing the group, body, or numbers in order, selecting the body or numbers from the set, is known as combinations in such a way that the order of the number does not matter. In mathematics, permutation is also known as the process of organizing a group in which all the members of a group are arranged into some sequence or order. The process of permuting is known as the repositioning of its components if the group is already arranged. Permutations take place, in almost every area of mathematics. They mostly appear when different commands on certain limited sets are considered. Permutation Formula In permutation r things are picked from a group of n things without any replacement. In this order of picking matter.
Combination A combination is a function of selecting the number from a set, such that (not like permutation) the order of choice doesn’t matter. In smaller cases, it is conceivable to count the number of combinations. The combination is known as the merging of n things taken k at a time without repetition. In combination, the order doesn’t matter you can select the items in any order. To those combinations in which re-occurrence is allowed, the terms k-selection or k-combination with replication are frequently used. Combination Formula In combination r things are picked from a set of n things and where the order of picking does not matter.
How many words of 3 vowels and 6 consonants can be formed taken from 5 vowels and 10 consonants?Answer:
Similar Questions Question 1: If 5 vowels and 6 consonants are given, then how many 6 letter words can be formed with 3 vowels and 3 consonants? Answer:
Question 2: How many different words each containing 3 vowels and 5 consonants can be formed with 5 vowels and 19 consonants? Answer:
Question 3: How many different words each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants? Answer:
Question 4: How many different words each containing 2 vowels and 3 consonants can be formed with 4 vowels and 7 consonants? Answer:
How many different words each containing 2 vowels and 3 consonants can be formed with 5 vowels and?So, total number of words = 5C2× 17C3×5! =816000.
How many different words each containing 2 vowels and 3 consonants can be formed with five vowels and 17 consonants?=6800×120=816000.
How many words of 3 consonants and 2 vowels can be formed out of 7 consonants and 4 vowels?Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is equal to? = 210.
How many words of 3 consonants and 2 vowels can be formed out of 5 consonants and 3 vowels?Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters. = 5! = 120.
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