More questions:-
(8) A committee of 12 is to be selected from 10 men and 10 wom
In how many ways can the selection 'be carried out
(1) If there are no restriction
(2) There must be 6 men and 6 women
(3) there must be even number
of women
4) There must be more women than men
(5) There must be at least 8
men.
Answers
Answer:
1. total no.of people = 10+10 = 20
From this 20 we should select any 12 members
So the answer is 20c12 ways.
2. 6 men from 10 men and 6 women from 10 women. So, 10c6 * 10c6 ways.
3. the question is even number of women. so it could be 0, 2, 4, 6, 8, 10, or 12 women.
case 1: 0 women, 12 men ------ not possible because there are only 10 men.
case 2: 2 women, 10 men ----- 10c2 * 10c10 = 45.
case 3: 4 women, 8 men --- 10c4 * 10c8
case 4: 6 women, 6 men ---- 10c6 * 10c6
case 5: 8 women, 4 men ---- 10c8 * 10c4
case 6: 10 women, 2 men ---- 10c10 * 10c2 = 45.
case 7: 12 women, 0 men ---- impossible.
So the answer is adding all the cases.
90 + 10c4 * 10c8 * 2 + 10c6 * 10c6 ways.
4. More women than men. so number of women could be 7, 8, 9 or 10.
case 1: 10c7 * 10c5 ways
case 2: 10c8 * 10c4 ways
case 3: 10c9 * 10c3 ways
case 4: 10c10 * 10c2 ways
Adding all these cases gives you the answer.
5. Atleast 8 men. so the number of men could be 8, 9 or 10.
case 1: 10c8 * 10c4 ways
case 2: 10c9 * 10c3 ways
case 3: 10c10 * 10c2 ways
Adding all these cases gives you the answer.
Hope this is helpful.