MHT CET · Maths · Permutation Combination
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
- A 240
- B 186
- C 60
- D 120
Answer & Solution
Correct Answer
(B) 186
Step-by-step Solution
Detailed explanation
The committee can be formed in following ways:
(5 men), (4 men, 1 lady) , (3 men, 2 ladies)
\(\therefore\) Number of was \(=\left({ }^6 \mathrm{C}_5\right)+\left({ }^6 \mathrm{C}_4 \times{ }^4 \mathrm{C}_1\right)+\left({ }^6 \mathrm{C}_3 \times{ }^4 \mathrm{C}_2\right)\)
\(=(6)+(15 \times 4)+(20 \times 6)=6+60+120=186\)
(5 men), (4 men, 1 lady) , (3 men, 2 ladies)
\(\therefore\) Number of was \(=\left({ }^6 \mathrm{C}_5\right)+\left({ }^6 \mathrm{C}_4 \times{ }^4 \mathrm{C}_1\right)+\left({ }^6 \mathrm{C}_3 \times{ }^4 \mathrm{C}_2\right)\)
\(=(6)+(15 \times 4)+(20 \times 6)=6+60+120=186\)
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