Has 11 identical coins. he wants to give some of them to 3 beggars and keep the remaining for himself, then number of different ways to do so is (he may keep all of them)
Answers
Given : Shyam has 11 identical coins.
He wants to give some of them to 3 beggars and keep the remaining for himself
To Find : number of different ways to do so
Solution:
Keeps 11
1 way
Keep 10
3 Ways ( 1 coin to Either of three)
Keep 9
6 ways ( 2 coins to Either of three , one coin each to any two )
Keep 8
10 ways ( 1 coins to Each , 3 coins Either one of three , 2 coins to Either two of three , two coins to any one of three and one coin each to other two )
and so on
ⁿ⁺¹C₂ n = 12 hence last ¹³C₂ = 78
1 + 3 + 6 + 10 + 15 + 21 + .................................. + 78
= 364
364 Ways
Direct formula
n + r C r
n = 11 ( objects )
r = 3
11 + 3 = 14
¹⁴C₃ = 364
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