Problem Solving

Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?

Please explain, thank
OA: 21
Source : Gmat-maths.blocked

5,0,0
0,5,0
0,0,5

1,1,3
1,3,1
3,1,1

1,2,2
2,1,2
2,2,1

3,2,0
2,3,0
0,3,2
0,2,3
3,0,2
2,0,3

0,1,4
0,4,1
4,1,0
1,4,0
4,0,1
1,0,4


21

There's another way of doing this without writing all the answer options..

Just write the different ways you can distribute 5 donuts..

a. 1, 2, 2 can be arranged in 3!/2! ways
b. 3, 2, 0 can be arranged in 3! ways
c. 4, 1, 0 can be arranged in 3! ways
d. 5, 0, 0 can be arranged in 3!/2! ways
e. 1, 1, 3 can be arranged in 3!/2! ways

Since we have to distibute donuts.. 0, 0, 0 is not an option, although 0 is a whole number.

Total ways = a + b + c + d + e = 21

Brent,

Isn't this similar to one of the problems you created?? I remember you created one and there was a trick to it, but I don't quite remember what it was.

Brent Hanneson wrote:

There it is!! I knew it was something like that but couldn't quite remember!

Brent Hanneson wrote:

Damn cool man!! Nice approach.. I liked it a lot.. super..