You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this? (it's not 15)

20

Step-by-step explanation:

I guess that we want to distribute all the 7 candies between 4 kids

We have 3 options:

first 3, 2, 1 and 1. (the number of candies that each kid gets)

The possible permutations in this case:

if we leave the 3 fixed, the ones do are equal, so the permutations are only given by the change in the kid that gets 2 candies, we have 3 permutations for this.

And for the fixed 3, we have 4 possible places where we can fix it, so the total number of combinations is:

c = 3*4 = 12.

and the second option is (2, 2, 2, 1)

Here the only change is the kid that gets only one candy, we have 4 options in this case:

c = 4.

the third option is (4, 1, 1, 1)

Here the only change is the kid that gets 4 candies, and we have 4 options for this, so we have 4 combinations:

c = 4.

Then the total number of possible combinations is:

C = 12 + 4 + 4 = 20