WAEC 2011 · Paper 2 · Q6

(a)
Evaluate $\dfrac{{}^9P_3}{{}^{15}C_3} + \dfrac{{}^5C_3}{{}^3P_2}$ , correct to two decimal places.
(b)
A committee of 2 tutors and 5 pupils is to be formed among 6 tutors and 10 pupils. In how many ways can this be done, if one particular tutor must be on the committee and two particular pupils must not be on the committee?

Worked solution (try it first)

Work out each symbol: $\,{}^9P_3 = 9 \times 8 \times 7 = 504$ and $\,{}^{15}C_3 = \dfrac{15 \times 14 \times 13}{6}$
$= 455$ .
$\,{}^5C_3 = 10$ and $\,{}^3P_2 = 3 \times 2 = 6$ .
So the value is $\dfrac{504}{455} + \dfrac{10}{6} = 1.1077 + 1.6667$
$= 2.7744$ , which is $2.77$ to two decimal places.