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

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Quantrex Academy · Accepted Answer

Correct answer: C. 485

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 .

A man has 7 relatives ( 4 women and 3 men). His wife also has 7...

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