Question

Consider the word W = SOLICITATION consisting of 6 vowels namely three I's, one A's and two O's and 6 consonants namely two T's and C, L, N, S one each. Words are formed using only the letters from the word W.
If the number of words that can be made by using all the letters of the word W, if O's as well as I's are separated is N(8!), then the value of N is

• A. 158
• B. 228
• C. 260
• D. None

Answer 1

Answer: (A)

Vowels" $I = 3; A = 1; O = 2 $
Consonants:$ S = 1; L = 1 : C = 1 ; N = 1 ; T = 2$
Number of words when I's separated
$\frac{9 !}{2 ! 2 !} \cdot{ }^{10} C _3 \cdot 1$
and number of words when I's separated and O's together
$ \frac{8 !}{2 !} \cdot{ }^9 C _3 \cdot 1 $
$\therefore \text { Total }=\frac{9 !}{2 ! 2 !} \cdot{ }^{10} C _3-\frac{8 !}{2 !} \cdot{ }^9 C _3=228 \times 8 ! \Rightarrow N =228$