A committee of five is to be chosen from a group of $8$ people which include a married couple. The probability for the selected committee which may or may not have the married couple is.

(a)

\frac{13}{28}

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(b)

\frac{5}{14}

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(c)

\frac{1}{56}

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(d)

\frac{3}{56}

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Solution

The correct option is A (a) $\frac{13}{28}$
Total number of ways to select= ${8_{C}}_{5}$ =56
case i)Includes the married couple than we have to choose 3 from 6 remaining people = ${6_{C}}_{3}$ =20
case ii)Doesn't Includes the married couple than we have to choose 5 from 6 remaining people = ${6_{C}}_{5}$ =6
Total favourable ways=26
Probability=26/56=13/28

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A committee of five is to be chosen from a group of 8 people which include a married couple. The probability for the selected committee which may or may not have the married couple is.

A committee of five is to be chosen from a group of $8$ people which include a married couple. The probability for the selected committee which may or may not have the married couple is.