(a) If \(^{18}C_{r} = ^{18}C_{r + 2}\), find \(^{r}C_{5}\). (b) In a community, 10% of the people tested positive to the HIV virus. If 6 persons from the co...

(a) If \(^{18}C_{r} = ^{18}C_{r + 2}\), find \(^{r}C_{5}\).

(b) In a community, 10% of the people tested positive to the HIV virus. If 6 persons from the community are selected at random, one after the other with replacement, calculate, correct to four decimal places, the probability that : (i) exactly 5 (ii) none (iii) at most 2; tested positive to the virus.