Question

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)

Answer 1

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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