A man has 5 friends and his wife has 4 friends. They want

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A man has 5 friends and his wife has 4 friends. They want to invite either of their friends, one or more to a party. In how many ways can they do so ?

1. 9
2. 18
3. 31
4. 46

Correct Option: D

Number of ways of selecting one or more friends from 5 friends
= ⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅
= 5 + 10 + 10 + 5 + 1
= 31 ways
Number of ways of selecting one or more friends from 4 friends = ⁴C₁ + ⁴C₂ + ⁴C₃ + ⁴C₄
= 4 + 6 + 4 + 1
= 15 ways
∴ Total number of ways = 31 + 15 = 46 ways