Question

A group of 3 men and 3 women went to the movies. How many ways can you sit in a row of 6 chairs if men want to sit together and women want to sit together?

Answer 1

There are 6 people. If they sit in a row, the 3 woman can sit in the 2 ends of 6 seats,

since they can sit together so that there is 2 ways

W, W, W , M , M , M

or M , M , M, W ,W ,W

So, 2 positions to put the group of women. and if women sit together then men will be sit together automativ]cally

Then, the women can be ordered in 3! = 6 ways. The men can also be ordered in 3! = 6 ways.

So, the answer is 2 × 6 × 6 = 72.

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