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  • A committee of 4 person is to be formed from 2 ladies , 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young me

A committee of 4 person is to be formed from 2 ladies , 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men . Then the total number of ways in which this committe can be formed is :

Option: 1

40


Option: 2

41


Option: 3

16


Option: 4

32


Answers (1)

best_answer

2 \text{ lady} +2\text{ old men}+4 \text{ young men}

Case 1

0 young men 2 old men and 2 lady

Case 2

1 young men 1 old men and 2 lady

Case 3

1 young men 2 old men and 1 lady

Case 4

2 young men 1 old men and 1 lady

Hence

{\color{Red} (0 \;YM+2 L+2\;OM)+(1 \;YM+ 1 L+ 2\;OM)+ (1\;YM+1 L+\;1OM)+(2\;YM+1 L+1\;OM)}

=(\;^4C_{0} \cdot \;^2C_{2} \cdot\;^ 2C_{2})+(\;^4C_{1}\cdot\;^2C_{1}\cdot\;^{2} C_{2})+(\;^4 C_1\cdot\;^ 2C_{2} \cdot \;^2C_1)+\left (\;^4C_{2} \cdot \;^2C_1 \cdot\;^ 2C_1 \right )

=1\cdot 1\cdot 1+4 \cdot 2 \cdot1+4 \cdot 1 \cdot 2+6 \cdot 2 \cdot 2

=1+8+8+24=41

Posted by

Rakesh

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