a man has 6 friends. in how many ways may he invite one or more of them in a dinner?

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# A man has 6 friends in how many ways may he invite one or more of them in a dinner?

So, the number of ways he could do this is:

- Invite only one friend
- Invite any two friends
- Invite any three friends
- Invite any four friends
- Invite any five friends
- Invite all six friends

This can be thought of in terms of combinations. Inviting r friends out of n is same as choosing r friends out of n. So, we can write the possibilities as:

6C1+6C2+6C3+6C4+6C5+6C6

=6+15+20+15+6+1

=63

Therefore, there are 63 ways in which he can invite 1 or more friends out of his 6 friends.