NIMCET 2018 Question Paper with solutions

Given that,
Student council has total numbers = 10
To select one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members from 10 members
Firstly, we have to select 6 members from 10 members. Which can be done in total number of ways = $\stackrel{10}{}{\mathit{C}}_6$
But there are two Executive (repetition) members
∴ That number of ways will be = $\frac{6!}{2!}$
Hence, total number of ways in which we can appoint threemembers = $\stackrel{10}{}{\mathit{C}}_6$ × $\frac{6!}{2!}$
= $\frac{10!}{4!6!}\times \frac{6!}{2!}$ $\left[\stackrel{\mathit{c}}{}{\mathit{C}}_{\mathit{r}}=\frac{\mathit{n}!}{\left(\mathit{n}-\mathit{r}\right)!\mathit{r}!}\right]$
= $\frac{10\times 9\times 8\times 7\times 6\times 5}{2}$ = 10 × 9 × 8 × 7 × 5 × 3 = 75600