Theory question 106
Permutations and CombinationsA committee of 3 is formed from a panel of 5 men and 3 women. Find the: (a) number of ways of forming the committee; (b) probability that at least one woman is on the committee.
Show the model answer
Model answer
(a) ⁸C₃ = 56 ways.
(b) No woman: ⁵C₃ = 10, so P(at least one woman) = 1 − 10/56 = 46/56 = 23/28.
Explanation
'At least one' = 1 − P(none).