In a box containing 15 bulbs, 5 are defective. If 5 bulbs are selected at random from the box, find the probability of the event, that
i) none of them is defective
ii) only one of them is defective
iii) atleast one of them is defective

Total no.of bulbs $=15$
Defective bulbs $=5$
Good bulbs $=10$
5 bulbs are selected at random $n\left(S\right){=}^{15}{C}_5$

i)  Probability of none of them is defective $=\frac{{ }^{10}{C}_5}{{ }^{15}{C}_5}$

ii) $E$ be the event of only one of them is defective  $n\left(E\right){=}^5{C}_1{\times }^{10}{C}_4$

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{{ }^5{C}_1{\times }^{10}{C}_4}{{ }^{15}{C}_5}$

iii) $P$(at least one of them is defective)

$1-p$ (none of them is defective)  $=1-\frac{{ }^{10}{C}_5}{{ }^{15}{C}_5}$