A) 485
B) 500
C) 486
D) 102
Correct Answer: A
Solution :
The possible cases are Case I: A man invites 3 ladies and woman invites 3 gentlemen \[\Rightarrow \] \[^{4}{{C}_{3}}{{.}^{4}}{{C}_{3}}=16\] Case II: A man invites (2 ladies, 1 gentleman) and women invites (2 gentlemen, 1 lady) \[\Rightarrow \] \[{{(}^{4}}{{C}_{2}}{{.}^{3}}{{C}_{1}}).{{(}^{3}}{{C}_{1}}{{.}^{4}}{{C}_{2}})=324\] Case III: A man invites (1 lady, 2 gentlemen) and women invites (2 ladies, 1 gentleman) \[\Rightarrow \] \[{{(}^{4}}{{C}_{1}}{{.}^{3}}{{C}_{2}}).{{(}^{3}}{{C}_{2}}{{.}^{4}}{{C}_{1}})=144\] Case IV: A man invites (3 gentlemen) and women invites (3 ladies) \[\Rightarrow \] \[^{3}{{C}_{3}}{{.}^{3}}{{C}_{3}}=1\] \[\therefore \]Total number of ways \[=16+324+144+1=485\]You need to login to perform this action.
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