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  4. A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes atleast 1 lady, atleast 1 old man and atmost 2 young men. Then the total number of ways in which this committee can be formed is

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Q. A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes atleast 1 lady, atleast 1 old man and atmost 2 young men. Then the total number of ways in which this committee can be formed is

Permutations and Combinations

Solution:

Total number of ways $=\left({ }^2 C _2 \times{ }^2 C _2 \times{ }^4 C _0\right)+2\left({ }^2 C _1 \times{ }^2 C _2 \times{ }^4 C _1\right)+\left({ }^2 C _1 \times{ }^2 C _1 \times{ }^4 C _2\right)$
$= 1 + 2(8) + 24 = 41$