How many ways can you give 10 apples to 4 friends if each friend gets at least one apple?

So, (10+4–1)C(4–1)=286 ways.

How many ways can 5 apples identical be distributed among 4 children some children may get no apples?

Similarly, in the case of {4, 1, 0, 0}, we will get 4!/2! = 12 arrangements (since 2 objects are identical) i.e. 5 apples can be distributed among 4 children by giving 4 apples to one child and 1 apple to another child in 12 ways.

How many ways are there to distribute seven distinct applies and six distinct pears to three distinct people such that each person has at least one pear?

There are then 36−3⋅26+3=540 possible ways to distribute the pears.

How many ways can you distribute 7 distinct apples?

The same answer 540 will come in this process too.

How many different ways can you distribute the apples?

As you say, you can break this into multiplication principle by first distributing the apples, and then distributing the pears and multiplying the results. You correctly found 3 7 as the number of ways of distributing the apples. Now we ask how to distribute the pears such that everyone gets at least one.

How many apples can be distributed to 4 children?

In the question given that 12 apples & 4 children’s & the condition is each 1 get 2 apples (may be 2 or more) ,firstly we can distribute in the way that each one can get 2apples=2×4=8…… There are 4 apples remaining&now we can distribute 4 apples among 4childrens there is no condition they may get 0,1,2,3,4…

How many possible ways could the pears be distributed?

There are then 3 6 − 3 ⋅ 2 6 + 3 = 540 possible ways to distribute the pears. Multiplying by the number of ways we could distribute the apples, we arrive at a total of 3 7 ⋅ 540 = 1180980

How do you find the distribution of apples to bins?

For instance, AA*A*A represents the distribution (2,1,1), where Kathy gets two apples and the other two children get one each. Sequence AAA*A* represents the situation (3,1,0), where Kathy gets three, Peter gets one, and Susan gets none. Thus, each distribution of apples to bins is associated with a unique string of 4A’s and 2 *’s.