Question

7 relatives of a man comprises 4 ladies and 3 gentlemen; his wife has also 7 relative; 3 of them are ladies and 4 gentlemen.

Answer 1

The possible cases are:

Case I : A man invites (3 ladies) and woman invites (3 gentlemen)

⁴C₃ ⁴C₃ = 16

Case II : A man invites (2 ladies,1 gentleman) and woman invites (2 gentleman, 1 lady)

(⁴C₂³C₁)(³C₁⁴C₂) = 324

Case III :   A man invites (1 lady, 2 gentlemen) and woman invites (2 ladies, 1 gentleman)

⇒ (⁴C₁³C₂)(³C₂⁴C₁) = 144

Case IV :   A man invites (3 gentlemen) and woman invites (3 ladies)

³C₃ ³C₃ = 1

Total number of ways

= 16 + 324 + 144 + 1 = 485

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