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
${}^4{C}_2\times 21\times 8=6\times 21\times 8=126\times 8=1008$