1. 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? I will mark as Brainlist!
Answers
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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Answer:
64
Step-by-step explanation:
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