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Question: A committee of five is to be chosen from a group of 9 people. The probability that a certain married...

A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all, is

A

½

B

5/9

C

4/9

D

2/9

Answer

4/9

Explanation

Solution

Required probability = 7C39C5+7C59C5=56126=49\frac { { } ^ { 7 } \mathrm { C } _ { 3 } } { { } ^ { 9 } \mathrm { C } _ { 5 } } + \frac { { } ^ { 7 } \mathrm { C } _ { 5 } } { { } ^ { 9 } \mathrm { C } _ { 5 } } = \frac { 56 } { 126 } = \frac { 4 } { 9 }