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

To split the cookies among the three kids, use a combination of stars and bars. The number of ways is 78.

Step-by-step explanation:

To find the number of ways the cookies can be split among the three kids, we can use a combination of stars and bars. Let each cookie be represented by a star and introduce two bars to divide the cookies among the kids. The number of ways to split the cookies is then equal to the number of ways to arrange the 11 stars and 2 bars. This can be calculated using the formula for combinations: nCr = n! / (r!(n-r)!). In this case, n = 13 (11 stars + 2 bars) and r = 2 (the number of bars). Thus, the number of ways to split the cookies is 13C2 = 78.