From a group of 10 men and 5 women, four member committees are to be formed each of which must contain atleast one woman. then the probability for these committees to have more women than men, is
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Number of men = 10
Number of women= 5
Total no of possible cases
WOMEN MEN
1. 5c1 * 10c3 =600
2. 5c2 * 10c2 =450
3. 5c3 * 10c1 =100
4. 5c4 * 1 =5
Here only case 3 and 4 are favourable as per the condition that the Number of women should be more than men
Hence the no of favourable outcomes is 105 (100 +5)
The total no of outcomes is 1155 (600+400+100+5)
Now , the probability is = 105/1155
= 1/11
Hence the probability is 1/11
Number of women= 5
Total no of possible cases
WOMEN MEN
1. 5c1 * 10c3 =600
2. 5c2 * 10c2 =450
3. 5c3 * 10c1 =100
4. 5c4 * 1 =5
Here only case 3 and 4 are favourable as per the condition that the Number of women should be more than men
Hence the no of favourable outcomes is 105 (100 +5)
The total no of outcomes is 1155 (600+400+100+5)
Now , the probability is = 105/1155
= 1/11
Hence the probability is 1/11
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