A man has 5 male and 4 female relatives. His wife has 4 male and 5 female relatives. The number of ways in which they can invite 5 male and 5 female relatives so that 5 of them are man’s relatives and remaining 5 are his wife’s relatives

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5426

5226

5526

5626

answer is D.

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Detailed Solution

mans relatives		women relatives
men	women	men	women
5	0	0	5
4	1	1	4
3	2	2	3
2	3	3	2
1	4	4	1

No. of ways of muting

$= {(5 c_{5} \times c_{0})}^{2} + {(5 c_{4} \times 4 c_{1})}^{2} + {(5 c_{3} \times 4 c_{2})}^{2} + {(5 c_{2} \times 4 c_{3})}^{2} + {(5 c_{1} \times 4 c_{4})}^{2} = {(1 \times 1)}^{2} + {(5 \times 4)}^{2} + {(10 \times 6)}^{2} + {(10 \times 4)}^{2} + {(5 \times 1)}^{2} = 1 + 400 + 3600 + 1600 + 25 = 5626$