A committee of 5 is to be chosen from a group of 9 people.The probability that a certain married couple will serve either together or not at all?

1/5

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5/9

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2/9

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4/9

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Solution

The correct option is D
4/9

If the couples serve then 3 people can be selected in $^{7} C_{3}$ ways.

If the couples don't serve then 5 people can be selected in $^{7} C_{5}$ ways.

Favourable case: $^{7} C_{3} +^{7} C_{5} - - - (1)$

Sample Space: $^{9} C_{5} - - - (2)$

$P (E) = \frac{(1)}{(2)}$

$P (E) = \frac{4}{9}$

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A committee of 5 is to be chosen from a group of 9 people.The probability that a certain married couple will serve either together or not at all?

The correct option is D 4/9 If the couples serve then 3 people can be selected in 7C3 ways. If the couples don't serve then 5 people can be selected in 7C5 ways. Favourable case: 7C3+7C5−−−(1) Sample Space: 9C5−−−(2) P(E)=(1)(2) P(E)=49