Question

You have 50 of each of the following kinds of jellybeans: red, orange, green, yellow. The jellybeans of each color are identical.
(a)how many ways can you put all the jellybeans in a row?
(b)How many handfuls of 12 are possible?

Answer 1

Answer:-

Given that:-

You have 50 of each of the following kinds of jellybeans: red, orange, green, yellow. The jellybeans of each color are identical.
(a)how many ways can you put all the jellybeans in a row?

Total 200 Jelly Beans we are having. In those 50 are red, 50 are Orange, 50 are Green, 50 are Yellow.

Suppose we have n items, where there are n1,n2,…,nk that are identical. The number of ways to permute them is

n!/(n1!.n2!.n3!....nk!)

So, Total number of ways for arranging all the Jelly Beans in a row is

200!/50!*50!*50!*50!
(b)How many handfuls of 12 are possible?

We have 4 varieties. Red, Orange, Green, Yellow.

So, Total of all the varieties must be 12.

x1 + x2 + x3 + x4 = 12

So the answer for this problem is to arrange

****|**|***|* is a possible solution. Where we divided each color with a pipe.
(r+k-1)!
----------- = C(r+k-1,r)
r! (k-1)!
So the answer for this problem indirectly we can reuce to arranging 12 * and 3 | 's

So answer is = 15!/(12!*3!)