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Q.

A man has 7 relatives, 4 women and 3 men. His wife also has 7 relatives, 3 women and 4 men. The number of ways in which they can invite 3 men and 3 women so that they both invite three each is

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a

485

b

584

c

720

d

1024

answer is A.

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Detailed Solution

men relatives		women relatives		no of selections
women	men	women	men
3	0	0	3	$^{4} C_{3} .^{4} C_{3}$
2	1	1	2	$^{3} C_{1} .^{4} C_{2} .^{4} C_{2} .^{3} C_{1}$
1	2	2	1	$^{3} C_{2} .^{4} C_{1} .^{4} C_{1} .^{3} C_{2}$
0	3	3	0	$^{3} C_{3} .^{3} C_{3}$
$^{4} C_{3} .^{4} C_{3} +^{3} C_{1} .^{4} C_{2} .^{4} C_{2} .^{3} C_{1} +^{3} C_{2} .^{4} C_{1} .^{4} C_{1} .^{3} C_{2} +^{3} C_{3} .^{3} C_{3} = 485$

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