Permutations And Combinations Question 121

Question: How many words can be formed by taking 3 consonants and 2 vowels out of 5 consonants and 4 vowels

Options:

A) $ ^{5}C_3\times {{}^{4}}C_2 $

B) $ \frac{^{5}C_3\times {{}^{4}}C_2}{5} $

C) $ ^{5}C_3\times {{}^{4}}C_3 $

D) $ {{(}^{5}}C_3\times {{}^{4}}C_2)(5)! $

Show Answer

Answer:

Correct Answer: D

Solution:

  • The letters can be select in $ ^{5}C_3{{\times }^{4}}C_2 $ ways. Therefore the number of arrangements are $ {{(}^{5}}C_3{{\times }^{4}}C_2)5\ ! $ .