question_answer

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :                               JEE Main Solved Paper-2017

A)  484                                       

B)  485

C)  468                                       

D)  469

Correct Answer: B

Solution :

                Total number of ways \[{{\,}^{4}}{{C}_{0.}}.{{\,}^{3}}{{C}_{3}}.{{\,}^{3}}{{C}_{3.}}.{{\,}^{4}}{{C}_{0.}}.+\,{{\,}^{4}}{{C}_{1}}{{.}^{3}}{{C}_{2}}{{.}^{3}}{{C}_{2}}.{{\,}^{4}}{{C}_{1.}}\] \[+{{\,}^{4}}{{C}_{2.}}.{{\,}^{3}}{{C}_{1}}.{{\,}^{3}}{{C}_{1.}}.{{\,}^{4}}{{C}_{2.}}.+\,{{\,}^{4}}{{C}_{3}}{{.}^{3}}{{C}_{0}}{{.}^{3}}{{C}_{0}}.{{\,}^{4}}{{C}_{3}}\] \[=485\]