(Q). A committee of 5 men & 5 women is to be selected from 9 men & 10 women.
(i). In how many ways this can be done
(ii). In how many ways this can be done if a particular woman is always selected
(iii). In how many ways this can be done if a particular woman is always selected and a man is always rejected?
Solution:-
(i).
5 men can be selected out of 9 men in ⁹C₅ ways
⟹ 5 women can be selected out of 10 women in ¹⁰C₅ ways
Hence number of ways to select 5 men & 5 women is = ⁹C₅×¹⁰C₅ Answer
(ii).
if a particular woman is always selected then this can be done in ⁹C₄ ways
Hence number of ways = ⁹C₅×⁹C₄ Answer
(iii).
If a particular woman is always selected then this can be done in ⁹C₄ ways
⟹ if a particular man is always rejected then this can be done in ⁸C₅ ways
Hence number of ways = ⁹C₄×⁸C₅ Answer