Question

A person has 6 friends. Over
several days he invites some of them to a
dinner party so that the company never
repeats (he may, for example, invite nobody
on one of the days). For how many days can
he follow this rule?

Answer 1

Given : A person has 6 friends. Over  several days he invites some of them to a  dinner party so that the company never  repeats .

To Find : For how many days can  he follow this rule

Solution:

Friends = 6

All 6 friends can be invited  in  ⁶C₆  = 1  Way

5 friends can be invited  in  ⁶C₅  = 6  Ways

4 friends can be invited  in  ⁶C₄  = 15  Ways

3 friends can be invited  in  ⁶C₃  = 20  Ways

2 friends can be invited  in  ⁶C₂  = 15  Ways

1 friend can be invited  in  ⁶C₆  = 6  Ways

0 friends can be invited  in  ⁶C₀  = 1  Way

Total  =  1 + 6 + 15  + 20 + 15 + 6 + 1   =  64

or ( ⁶C₀ + ⁶C₁ +....................+ ⁶C₅ + ⁶C₆) = 2⁶  = 64

For 64 days he can follow this rule

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