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.
Number of 4 lettered word that can be made if each word contains exactly 2 consonants and exactly 2 vowels, is

• A. 1008
• B. 504
• C. 1056
• D. 168

Answer 1

Answer: (A)

Vowels" $I = 3; A = 1; O = 2 $
Consonants:$ S = 1; L = 1 : C = 1 ; N = 1 ; T = 2$
2 consonants can be selected in
${ }^2 C _2+{ }^5 C _2=1+10=11$
number of arrangement of 2 consonants
$=1+10 \times 2 !=21$
2 vowels can be selected in
${ }^2 C _1+{ }^3 C _2=5$
and arrangement is $2+3 \times 2 !=8$
$\therefore $ Number of 4 letter words
${ }^4 C _2 \times 21 \times 8=6 \times 21 \times 8=126 \times 8=1008$