Question

A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have

1. No woman
2. One man
3. No man

Answer 1

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`