Question

The number of five letter words containing 3 vowels and 2 consonants that can be formed using the letters of the word EQUATION so that two consonants occur together is

• A. ${}^5{C}_3{}^3{C}_{5}5!$
• B. ${}^5{C}_3{}^3{C}_{5}2!3!$
• C. ${}^5{P}_3{}^3{P}_{2}5!$
• D. ${}^5{C}_3{}^3{C}_{2}2!4!$

Answer 1

The correct option is D ${}^5{C}_3{}^3{C}_{2}2!4!$

Vowels (A,E,I,O,U) five, consonants (Q,T,N) three
3 vowels can be chosen in ${}^5{C}_3$ ways
2 consonants can be chosen in ${}^3{C}_2$ ways
2 consonants can be arranged in 2! Ways
3 vowels + 2 consonants bundle = 4 can be arranged in 4! Ways. $\therefore$ required number words ${=}^5{C}_3^3{C}_{2}2!4!$