Saturday, March 13, 2021

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

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:

  1. Invite only one friend
  2. Invite any two friends
  3. Invite any three friends
  4. Invite any four friends
  5. Invite any five friends
  6. 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.

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