Test Index

Probability

Section: Mathematics

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Question : 5 of 92

Marks: +1, -0

A four member committee is to be formed from a group containing 9 men and 5 women. If a committee is formed randomly, then the probability that it contains atleast one woman is

[AP EAPCET 23 May 2025 S2]

$\;\;\frac{125}{143}$
$\;\;\frac{18}{143}$
$\;\;\frac{60}{143}$
$\;\;\frac{65}{143}$

Solution:

Total people

=14(9 M +5 W)

Total ways to choose 4 peoples from 14 is

{}^{14}C_4

Total ways to choose all men is

={}^{9}C_4

So, total ways to choose atleast one women

\;={}^{14}C_4-{}^{9}C_4=\;\frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1}-\;\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}

\;=1001-126=875

Hence, required probability

=\;\frac{875}{1001}=\;\frac{125}{143}

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