Question 980630
A committee of seven members is to be formed from a group of 11 members. The probability that a certain married couple will either serve together or neither serves.
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The numerator is the number of ways they serve together or neither serves.

Case 1. They serve together.

Then we choose the remaining 5 to serve from the remaining 9 in 9C5 ways.

Case 2. Neither serves. Then we choose the 7 to serve from the remaining 9
in 9C7 ways.

Total successful ways: 9C5 + 9C7 = 126+36 = 162

Total ways to choose any 7:  11C7 = 330

Probability = 162/330 = 27/55

Edwin</pre>