Consider the Word W=TERRORIST.
Q. Number of four letter words that can be made using only the letters from the word W, if each word must contains atleast one vowel, is

Options

A. 588
B. 504
C. 294
D. 600

Answer

A

Explanation

There are 9 letters
T,T,R,R,R,E,O,I,S
`lamda`=Number of four lettered words (no restriction)
=Coefficient of `x^(4)` in
`4!(1+(x)/(1!)+(x^(2))/(2!))(1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!))(1+x)^(4)=626`
`mu=`Number of four lettered words (no vowels)
=Coefficient of `x^(4)` in
`4!(1+(x)/(1!)+(x^(2))/(2!))(1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!))(1+x)=38`
`therefore`Required ways (atleast one vowel)=626-38=588