Find the value of 4!

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