A committee of 5 is to be chosen from 6 men and 5 women. In how many ways if (a) it has exactly 2 women, (b) it has at least 1 woman? (c) How many arrangements of COLOMBO are there?
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Decide: order or no order? Committees: order doesn't matter, so use combinations. Arranging letters: use permutations.
2 · (a) Exactly 2 women. Choose 2 of 5 women and 3 of 6 men: 5C2 × 6C3 = 10 × 20 = 200.
3 · (b) Use the complement. Total committees 11C5 = 462. All-men committees 6C5 = 6.
4 · Subtract. At least 1 woman = 462 − 6 = 456.
5 · (c) Repeated letters. 7 letters, O three times: 7! ÷ 3! = 5,040 ÷ 6 = 840.
6 · Business link. The same counting fixes how many shortlists an HR panel at a Sri Lankan firm could form.
