NIMCET 2018 — Mathematics PYQ

Concept

${}^n{P}_r=\frac{n!}{(n-r)!}$  

Calculations

\text{Given, a student council has 10 members. From this, one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected.}  

$\Rightarrow$ 6 members are elected out of 10 members.  

\text{Number of ways to be elected 6 members out of 10 members}  
$={}^{10}{P}_6$  

$=\frac{10!}{(10-6)!}$  

$=\frac{10!}{4!}$  

$=\frac{4!\times 5\times 6\times 7\times 8\times 9\times 10}{4!}$  

$=151200$