In how many ways can 6 identical coins be distributed among Alex, Bea,
[#permalink]
03 Jul 2017, 00:09
Since some people can receive zero coins,
there are 3 ways of distributing the coins when 2 of them receive zero coins
A,B,C
6,0,0
0,6,0
0,0,6
Total : 3 ways
When one of them receives zero coin, the other two can receive {(1,5),(2.4)} coins
there are 6 ways of distributing each of these coins among A,B and C
A,B,C
1,5,0
5,1,0
1,0,5
5,0,1
0,1,5
0,5,1
This same pattern re-occurs for number (2,4)
When one of them receives zero coin, the other two can receive (3,3) coins
but there are 3 ways of distributing each of these coins among A,B and C
A,B,C
3,3,0
0,3,3
3,0,3
Total : 12 + 3 = 15 ways
When neither of them receives zero coins, they can be distributed in 2 ways.
(1,1,4) in 3 ways and (1,2,3) in 3!(6) ways
Total : 9 ways
There is one way of arranging the coins such that each of them has 2 coins.
(2,2,2)
Total : 1 way
Hence we have a total of 3+15+9+1 = 28 ways(Option C)