Seven men and seven women line up at a checkout counter in a

Seven men and seven women line up at a checkout counter in a store. In how many ways can they line up if the first person in line is a woman, and the people in line alternate woman, man, woman, man, and so on?

Solution

Probability of first person is a woman is 7/14
Probability of second person is a man is 7/13

Probability of third person is a woman is 6/12
Probabilityof fourth person is a man is 6/11

Probability of fifth person is a woman is 5/10
Probability of sixth person is a man is 5/9

Probability of seventh person is a woman is 4/8                                                                                              Probability of eight person is a man is 4/7

Probability of nineth person is a woman is 3/6                                                                                                    Probability of tenth person is a man is 3/5

Probability of eleventh person is a woman is 2/4                                                                                              Probability of twelth person is a man is 2/3

Probability of thirteenth person is a woman is 1/2                                                                                        Probability of forteenth person is a man is 1/1
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Multiply all these probabilities together and you get:
7/14*7/13*6/12*6/11*5/10*5/9*4/8*4/7*3/6*3/5*2/4*2/3*1/2*1/1 = 1/3432