In a group of 15 men, 9 are graduates. If 5 men are selected at
random, what is the probability that they consists of (i) all
graduates (ii) at least three graduates (iii) at most 2 graduates (iv)
exactly 4 graduates (v) no graduates?
Answers
Given : a group of 15 men, 9 are graduates.
5 men are selected at random
To Find : probability that they consists of
(i) all graduates (ii) at least three graduates (iii) at most 2 graduates (iv)
exactly 4 graduates (v) no graduates?
Solution:
group of 15 men
Graduates = 9
not graduates = 6
5 out of 15 can be selected in ¹⁵C₅ ways = 3,003
all graduates can be selected in ⁹C₅ ways = 126
Probability = 126/3003 = 42/1001 = 6/143
at least three graduates = ⁹C₃.⁶C₂ + ⁹C₄.⁶C₁ + ⁹C₅.⁶C₀
= 1260 + 756 + 126
= 2,142
Probability = 2,142/3003 = 714/1001 = 102/143
at most 2 graduates = ⁹C₀.⁶C₅ + ⁹C₁.⁶C₄ + ⁹C₂.⁶C₃
= 6 + 135 + 720
= 861
Probability = 861/3003 = 41/143
exactly 4 graduates = ⁹C₄.⁶C₁ = 756
probability = 756/3003 = 36/143
no graduates = ⁹C₀.⁶C₅ = 6
probability = 6/3003 = 2/1001
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