Question

Consider the 10 lettered word W = C U R R I C U L U M.
Number of ways in which all the letters of the word W can be arranged if vowels are to be separated is k (7!), then the value of k is equal to

• A. 5
• B. 4
• C. 3
• D. 2

Answer 1

Answer: (A)

First arrange consonants (R, R, C, C, L, M) in $\frac{6!}{2!2!}$ ways
Then number of gaps are 7 select 4 gaps out of 7 in ${}^7{C}_4$ ways then arrange 4 vowels (U, U, U, I) in these 4 gaps in $\frac{4!}{3!}$ ways.
$\therefore$ Total number of ways $=\frac{6!}{2!2!}\times \frac{7!}{4!3!}\times \frac{4!}{3!}=\frac{120}{4\times 6}\times 7!=5\times 7!$
$\therefore k=5$.