A corporation has 15 salesmen, 5 who are rated good, 7 average, and 3 poor. Three salesmen are selected randomly for their promotions. What is the probability that

1. Example
A corporation has 15 salesmen, 5 who are rated good, 7 average, and 3 poor. Three
salesmen are selected randomly for their promotions. What is the probability that
(i) All are good
(ii) Atmost one average
(iii) One of each kind.
Solution
5 are good
7 are average
3 are poor
(i) 𝑃(𝐴𝑙𝑙 𝑎𝑟𝑒 𝑔𝑜𝑜𝑑) =
𝑐3
5
𝑐3
15 =
10
455
= 0.0219
(ii) 𝑃(Atmost one average) = 𝑃(𝑥 = 0) + 𝑃(𝑥 = 1)
𝑃(Atmost one average) =
𝑐0
7
× 𝑐3
8
𝑐3
15 +
𝑐1
7
× 𝑐2
8
𝑐3
15
𝑃(Atmost one average) =
56 + 196
455
= 0.5538
(iii) 𝑃(One of each kind) =
𝑐1
5×𝑐1
7×𝑐1
3
𝑐3
15 =
105
455
= 0.2307