**The possible cases are:**

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

^{4}C_{3}^{ 4}C_{3} = 16

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

(^{4}C_{2}^{3}C_{1})(^{3}C_{1}^{4}C_{2}) = 324

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

⇒ (^{4}C_{1}^{3}C_{2})(^{3}C_{2}^{4}C_{1}) = 144

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

^{3}C_{3}^{ 3}C_{3} = 1

## Total number of ways

## = 16 + 324 + 144 + 1 = 485