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A committee of 4 persons is to be formed from 2 ladies 2 old man and 4 youngmen such that it includes at least 1 lady, at least one old man and at most 2 yougmen. Then the total number of ways in which this committee can be formed is

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answer is A.

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Detailed Solution

Ladies(2)	old men(2)	young men(4)	committies
1	1	2	$^{2} C_{1} \times^{2} C_{1} \times^{4} C_{2} = 24$
2	1	1	$^{2} C_{2} \times^{2} C_{1} \times^{4} C_{1} = 8$
1	2	1	$^{2} C_{1} \times^{2} C_{2} \times^{4} C_{1} = 8$
total number of committtes=24+8+8=40

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