Hi Grothen,Grothen wrote:How can i distribute 16 apples among 4 children such that everyone gets at least 3 apples ?
If everyone has to have at least 3 apples, it means 3 x 4 = 12 apples should be distributed to the 4 children.
Therefore we are left with 16 - 12 = 4 apples to assign to the 4 children.
The rephrased question is "How can I distribute 4 apples among 4 children?"
4 apples can be broken down as follow:
1,1,1,1 - each child get one apple
1,1,2 - 2 children get 1 each and 1 child gets 4
2,2 - 2 children get 2 apples
3,1 - one child gets 3 apples and one child gets 1 apples
4 - one child gets 4 apples
Find all the possibilties for the choices above.
1,1,1,1 - each child get one apple : (4x3x2x1)/(4x3x2x1)=1 way
1,1,2 - 2 children get 1 each and 1 child gets 4 : (4x3x2)/(2*1)=12 ways
2,2 - 2 children get 2 apples : (4x3)/(2x1) = 6ways
3,1 - one child gets 3 apples and one child gets 1 apples : (4x3)=12 ways
4 - one child gets 4 apples = 4/1=4 ways
Add possibilities: 1+12+12+6+4 = 35ways
