Question

Three kids, Alberto, Bernadette, and Carlos, decide to share 11 cookies. They wonder how many ways they could split the cookies up provided that none of them receive more than 4 cookies (someone receiving no cookies is for some reason acceptable to these kids).
How many ways do they find?

Answer 1

Using the arrangements formula, it is found that they find 46200 ways.

What is the arrangements formula?

The number of arrangements of n elements is given by:

$A_n = n!$

If they repeat in $n_1, n_2, \cdots, n_n$ ways, the number of arrangements is given by:

$A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2!\cdots n_n}$

In this problem, 11 elements are arranged with repetitions of 4, 3 and 3, hence:

$T = \frac{11!}{4!3!3!} = 46200$

They find 46200 ways.

More can be learned about arrangements at brainly.com/question/2259733