A man has 7 relatives ( 4 women and 3 men). His wife also has 7 relatives ( 3 women and 4 men). In how many ways can they invite 3 women and 3 men so that 3 of them are man's relatives and 3 of them are his wife's relatives?

Step-by-step solution

Total number of ways aligned &= ^4 C ₃ ^4 C ₃=4 4=16 &+ ^3 C ₁ ^4 C ₂ ^4 C ₂ ^3 C ₁ &=18 18=324 &+ ^3 C ₃ ^4 C ₀ ^4 C ₀ ^3 C ₃ &=1 1 1 1=1 &+ ^3 C ₂ ^4 C ₁ ^4 C ₁ ^3 C ₂ &=12 12=144 aligned Hence, they can invite total no. of ways =16+324+1+144=485 .