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A committee of 5 is to be formed out of 6 men and 4 ladies. The number of ways this can be done, when at most 2 ladies are include, is
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Verified Answer
The correct answer is:
186
The committee can be formed in following ways:
( 5 men), (4 men, 1 lady) , (3 men, 2 ladies)
$\begin{aligned}
& \therefore \text { Number of was }=\left({ }^6 \mathrm{C}_5\right)+\left({ }^6 \mathrm{C}_4 \times{ }^4 \mathrm{C}_1\right)+\left({ }^6 \mathrm{C}_3 \times{ }^4 \mathrm{C}_2\right) \\
& =(6)+(15 \times 4)+(20 \times 6)=6+60+120=186
\end{aligned}$
( 5 men), (4 men, 1 lady) , (3 men, 2 ladies)
$\begin{aligned}
& \therefore \text { Number of was }=\left({ }^6 \mathrm{C}_5\right)+\left({ }^6 \mathrm{C}_4 \times{ }^4 \mathrm{C}_1\right)+\left({ }^6 \mathrm{C}_3 \times{ }^4 \mathrm{C}_2\right) \\
& =(6)+(15 \times 4)+(20 \times 6)=6+60+120=186
\end{aligned}$
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