A select group of 4 is to be formed from 8 men and 6 women in such a way that the group must have atleast one woman. In how many different ways can it be done ?
The total number of people is 8+6 = 14
An easy way to calculate the number of ways of selecting atleast one woman is to calculate the opposite of it.
The total number of ways of selecting 4 people from a total of 14 is $$^{14}C_4 = 1001$$
The number of ways of selecting a group of all men (and no women) is $$^8C_4 = 70$$
Hence, the number of ways of selecting 4 people such that atleast one of them is a woman is $$1001-70 = 931$$
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