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Question
A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have
- No woman
- One man
- No man
Solution
Number of men = 3 and number of women = 2
Total number of selecting 2 persons out of 5 persons = 5C2
i. Number of selecting no women = Number of selecting 2 men out of 3 men = 3C2
∴ P(Committee will have no women) = `(3"C"_2)/(5"C"_2)`
= `((3 xx 2)/(2 xx 1))/((5 xx 4)/(2 xx 1))`
= `(6/2)/(20/2)`
= `6/20`
= `3/10`
ii. Number of ways of selecting one man and the other person as a women = 3C1 × 2C1 = 6
∴ P(Committee will have one man) = `6/(5"C"_2)`
= `6/10`
= `3/5`
iii. Number of ways of selecting no man = Number of ways of selecting 2 women = 2C2
∴ P(Committee will have no man) = `(2"C"_2)/(5"C"_2)`
= `1/10`
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