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 $=\frac{6 !}{2 ! 2 !} \times \frac{7 !}{4 ! 3 !} \times \frac{4 !}{3 !}=\frac{120}{4 \times 6} \times 7 !=5 \times 7 !$
$\therefore k =5$.