A women wants to distribute 12 identical cookies to her 5 children of different ages.
The youngest has to get at least 2 cookies while the rest at least 1.
In how many way can she do it ?
The answer is 210
My unsuccessful attempt was dividing the problem
first, we give 1 of the children 2 cookies and the rest 1 cookie.
She can do that in 1 way.
Then we are left with 12-6 = 6 cookies to distribute.
We calculate "6 choose 5".
Can some one help ?
Hello, Hitman6267!
A women wants to distribute 12 identical cookies to her 5 children of different ages.
The youngest has to get at least 2 cookies while the rest get at least 1.
In how many way can she do it?
(The answer is 210)
Place the 12 cookies in a row, leaving spaces between them.
. .
Distribute 4 "dividers" among the 11 spaces.
. . There are: . ways.
So that: .
. . represents . from the youngest to the oldest.
And that: .
. . represents
But this includes distributions in which the youngest gets only one cookie.
Very well, how many ways are there in which the youngest gets one cookie?
We have: .
And we must distribute 3 dividers among the 10 spaces.
. . There are: . ways.
Therefore, there are: . ways in which the youngest
. . gets at least 2 cookies and the others get at least one.