Question

The number of permutations of $n$ things taken $r$ at a time if 3 particular things always occur is

• A. $\frac{(n-3)!}{(n-r)!}r(r-1)(r-2)$
• B. $\frac{(n-3)!}{(r-3)!}$
• C. $\frac{(n-3)}{(n-r)}3$
• D. $\frac{(n-3)}{(r-2)}!$

Answer 1

Answer: (A)

$\frac{(n-3)!}{(n-r)!}r(r-1)(r-2)$

Required number of ways $=$ Selection of $(r-3)$ things from $(n-3)$ and arrange $r$ things

${=}^{n-3}{C}_{r-3}.r!=\frac{(n-3)!}{(n-r)!}r(r-1)(r-2)$