Question

In a jar there are red jelly beans and green jelly beans. In how many ways can you pick red jelly beans and the same number of green jelly​ beans?

Answer 1

Complete Question:

In a jar there are 19 red jelly beans and 10 green jelly beans. In how many ways can you pick 4 red jelly beans and the same number of green jelly​ beans?

Answer:

`Both = 813960`

Explanation:

Given

Red Jelly Beans = 19

Green = 10

Required

Select 4 out of 19 red jelly beans and 4 out of 10 green jelly beans

The keyword in the question is pick and this implies combination;

4 from 19 red jelly beans is calculated as follows

`^nC_r = (n!)/((n-r)!r!)`

Where n = 19 and r = 4

`^(19)C_4 = (19!)/((19-4)!4!)`

`^(19)C_4 = (19!)/(15!4!)`

`^(19)C_4 = (19 * 18 * 17 * 16 * 15!)/(15! * 4 * 3 * 2 * 1)`

`^(19)C_4 = (19 * 18 * 17 * 16)/(4 * 3 * 2 * 1)`

`^(19)C_4 = (93024)/(24)`

`^(19)C_4 = 3876`

Similarly;

4 from 10 green jelly beans is calculated as follows

`^(10)C_4 = (10!)/((10-4)!4!)`

`^(10)C_4 = (10!)/(6!4!)`

`^(10)C_4 = (10 * 9 * 8 * 7 * 6!)/(6! * 4 * 3 * 2 * 1)`

`^(10)C_4 = (10 * 9 * 8 * 7 )/(4 * 3 * 2 * 1)`

`^(10)C_4 = (5040)/(24)`

`^(10)C_4 = 210`

Ways of selecting both is calculated as follows

`Both = 3876 * 210`

`Both = 813960`