Relatives of a man comprise 4 ladies and 3 gentlemen, and his wife has also 7 relatives: 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of the man's relatives and 3 of

Question

Relatives of a man comprise 4 ladies and 3 gentlemen, and his wife has also 7 relatives: 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of the man's relatives and 3 of the wife's relatives?

Smart Achievers · Accepted Answer

(485)

3 gentlemen and 3 ladies may be chosen as follows:

Case	Man	Wife
Case I	3(L)	3(G)
Case II	2(L), 1(G)	2(G), 1(L)
Case III	1(L), 2(G)	2(L), 1(G)
Case IV	3(G)	3(L)

Required number of ways of inviting 3 ladies and 3 gentlemen to the party

$= {}^{4}C_{3} \times {}^{4}C_{3} + ({}^{4}C_{2} \times {}^{3}C_{1}) ({}^{3}C_{1} \times {}^{4}C_{2}) + ({}^{4}C_{1} \times {}^{3}C_{2}) ({}^{3}C_{2} \times {}^{4}C_{1}) + {}^{3}C_{3} \times {}^{3}C_{3}$

$= 16 + 324 + 144 + 1 = 485$

Solution

Q.
Relatives of a man comprise 4 ladies and 3 gentlemen, and his wife has also 7 relatives: 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of the man's relatives and 3 of the wife's relatives

Want Us to Email you About Special Offers & Updates?

Solution

Q. Relatives of a man comprise 4 ladies and 3 gentlemen, and his wife has also 7 relatives: 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of the man's relatives and 3 of the wife's relatives

Want Us to Email you About Special Offers & Updates?

Q.
Relatives of a man comprise 4 ladies and 3 gentlemen, and his wife has also 7 relatives: 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of the man's relatives and 3 of the wife's relatives