JAMB 1999 · UME · Q43

If $\dfrac{^6C_r}{^6P_r} = \frac16$ , find the value of $r$ .

Worked solution (try it first)

$^6P_r$ is $^6C_r$ multiplied by $r!$ (the ways to order the $r$ chosen items), so $\dfrac{^6C_r}{^6P_r} = \dfrac{1}{r!}$ .
So $\dfrac{1}{r!} = \dfrac16$ , which means $r! = 6$ .
$3! = 3 \times 2 \times 1 = 6$ , so $r = 3$ , option B.