Out of Seven Constants and Four Vowels, the Number of Words of Six GMAT Problem Solving

Question: Out of seven constants and four vowels, the number of words of six letters, formed by taking four consonants and two vowels is (Assume that each ordered group of letter is a word):

1. 210
2. 462
3. 151200
4. 332640
5. 332940

Correct Answer: C

Solution and Explanation:
Approach Solution 1:

4 consonants can be chosen out of 7 in \(^7C_4=^7C_3=\frac{7*6*5}{3*2*1}\)=35 ways
2 vowels can be chosen out of 4 in \(^4C_2=\frac{4*3}{2*1}\)=6 ways
These chosen letters can be arranged in 6! = 720 ways

Total number of ways = 35 * 6 * 720 = 151200 ways

Approach Solution 2:
As per the problem statement, number of ways =.7C4⋅ .4C2⋅ 6!
7!/4!3! ⋅ 4!/2!2! ⋅6! = (7!⋅6⋅5⋅4)= 30⋅7⋅6⋅5⋅4⋅3⋅2 = 151200

Total number of ways =151200 ways.

“Out of seven constants and four vowels, the number of words of six letters, formed by taking four consonants and two vowels is (Assume that each ordered group of letter is a word):”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers assist the candidates to go through several sorts of questions that will enable them to enhance their mathematical understanding.

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