A man has 6 friends.In how many ways can he invite one or more of them to a tea party?
Answers
1 friend can be selected out of 6 in 6C1 = 6 ways
2 friends can be selected out of 6 in 6C2 = 15 ways
3 friends can be selected out of 6 in 6C3 = 20 ways
4 friends can be selected out of 6 in 6C4 = 15 ways
5 friends can be selected out of 6 in 6C5 = 6 ways
6 friends can be selected out of 6 in 6C6 = 1 ways
Therefore the required number of ways (combinations) = 6 + 15 + 20 + 15 + 6 + 1 = 63
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Given: The number of friends, a man has= 6
To find The number of ways can he invite one or more of them to a tea party.
Solution: This problem is based on the topic combination in mathematics, where a man can invite one or more friends and that should be less than equal to 6. He can invite 1 friend or 2 friends or 3 friends or 4 friends or 5 friends or all the 6 friends.
The selection of 1 friend out of 6 in 6C₁= 6 ways.
The selection of 2 friends out of 6 in 6C₂= 15 ways.
The selection of 3 friends out of 6 in 6C₃= 20 ways.
The selection of 4 friends out of 6 in 6C4= 15 ways.
The selection of 5 friends out of 6 in 6C₅= 6 ways.
The selection of 6 friends out of 6 in 6C₆= 1 way.
∴ The total number of ways or combinations
= 6C₁+6C₂+6C₃+6C₄+6C₅+6C₆ ways
=6+15+20+15+6+1 ways
= 63 ways.
Hence the number of ways can he invite one or more of them to a tea party is 63.