Question

In: Statistics and Probability

200 identical toys are to be sent to 5 families (A, B, C, D, E). If...

200 identical toys are to be sent to 5 families (A, B, C, D, E). If each family must get at least 3 toys and the family “A” cannot have more than 30 toys, how many different ways are there to distribute the toys?

Expert Solution

Answer:

Given that:

200 identical toys are to be sent to 5 families (A, B, C, D, E). If each family must get at least 3 toys and the family “A” cannot have more than 30 toys, how many different ways are there to distribute the toys?

This is a case of multinomial theorem. Let the toys given to 5 families be a, b, c, d and e

Also ,

and so on ..

If we are given here that:

Therefore,

Therefore, we have here:

Where each one of them is greater than 1.

Therefore the number of solutions of the above equation is computed using the multinomial formula as:

Now let a > 30 toys that is a get more than 30 toys

Let

Therefore, X >= 1

Putting it in the above equation, we have here:

with each one of them:

Number of solutions of above equation using multinomial theorem:

Therefore the number of different ways to distribute the toys here is computed as:

orchestra answered 1 year ago

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