Question

The number of ways in which 13 gold coins can be distributed among three persons such that each one gets at least two gold coins is

Answer 1

This is a question on combination.

n identical things distributed in r groups :

Formula

[(n+r-1)C(r-1)]

we can analyze this as follows :

As everyone has two coins in three groups we are left with:

13-2 × 3 = 7 coins.

Now 7 coins in 3 groups

n = 7 , r = 3

[(7+3-1)C(3-1)]

= ⁹C₂ = 9! / (9 - 2)!2! = 36

= 36 ways.