Question

Suppose a lot of n objects having $n_1$ objects of one kind, $n_2$ objects are of second kind, $n_3$ objects of third kind, .... , $n_k$ objects of $k^{th}$ kind satisfying the condition $n_1+n_2....+n_k=n,$ then the number of possible arrangements/permutation of m objects out of this lot is the coefficient of $x^m$ in the expansion of $m!\prod \left\{\sum _{\lambda =0}^{a_1}\frac{x^{\lambda }}{\lambda !}\right\}$

The number of permutations of the letters of the word SURITI taken 4 at a time is

• A. 360
• B. 240
• C. 216
• D. 192

Answer 1

The correct option is D 192

Given word : SURITI

$I=2$ times

S,U,R,T=1-times

case - I ; All letters are different

Number of arrangement = ${}^5{C}_4\times 4!$

$=5\times 24$

$=120$

case - II ; two are different and two are same kind

Number of arrangement = ${}^4{C}_2\times \frac{4!}{2!}$

$=6\times \frac{24}{2}=72$

total arrangement = $120+72=192$