Question
Akshay has 7 relatives, 3 males and 4 females. His wife
twinkle also have 7 relatives, 3 females and 4 males. In how many ways can they invite 3 male and 3 females so that 3 of them are Akshay’s relatives and 3 of his wife twinkle?Solution
There are 4 possible cases 
The required number of ways = (4C3 × 4C3) + (3C1 × 4C2) × (4C2 × 3C1) + (3C2 × 4C1) × (4C1 × 3C2) + (3C3 × 3C3) = (4 × 4) + (3 × 6 × 6 × 3) + (3 × 4× 4 × 3) + (1 × 1) = 16 + 324 + 144 +1 = 485 ways.
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