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The number of different ways in which a man can invite one or more of his 6 friends to dinner is?
- a)30
- b)63
- c)120
- d)15
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The number of different ways in which a man can invite one or more of ...
He can invite any one friend in 6C1 ways = 6 ways:
He can invite any two friends in 6C2 ways = 15 ways
He can invite any three friends in 6C3 ways = 20 ways
He can invite any 4 friends in 6C4ways = 15 ways
He can invite any 5 friends in 6C5 ways = 6 ways
He can invite all the 6 friends in 6C6 ways= 1 way.
Since any one of these could happen total possibilities are, 6+15+20+15+6+1 = 63.
He can invite any two friends in 6C2 ways = 15 ways
He can invite any three friends in 6C3 ways = 20 ways
He can invite any 4 friends in 6C4ways = 15 ways
He can invite any 5 friends in 6C5 ways = 6 ways
He can invite all the 6 friends in 6C6 ways= 1 way.
Since any one of these could happen total possibilities are, 6+15+20+15+6+1 = 63.
Most Upvoted Answer
The number of different ways in which a man can invite one or more of ...
He can invite one or more friends by inviting 1 friend, or 2 friends or 3 friends, or all the 6 friends.
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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Community Answer
The number of different ways in which a man can invite one or more of ...
We will use the formula =( 2 )"n _1 = (2)"6 _1= 63 which is our answer.
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The number of different ways in which a man can invite one or more of his 6 friends to dinner is?a)30b)63c)120d)15Correct answer is option 'B'. Can you explain this answer?
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