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:

$Both = 813960$

Step-by-step 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

$^nC_r = \frac{n!}{(n-r)!r!}$

Where n = 19 and r = 4

$^{19}C_4 = \frac{19!}{(19-4)!4!}$

$^{19}C_4 = \frac{19!}{15!4!}$

$^{19}C_4 = \frac{19 * 18 * 17 * 16 * 15!}{15! * 4 * 3 * 2 * 1}$

$^{19}C_4 = \frac{19 * 18 * 17 * 16}{4 * 3 * 2 * 1}$

$^{19}C_4 = \frac{93024}{24}$

$^{19}C_4 = 3876$

Similarly;

4 from 10 green jelly beans is calculated as follows

$^{10}C_4 = \frac{10!}{(10-4)!4!}$

$^{10}C_4 = \frac{10!}{6!4!}$

$^{10}C_4 = \frac{10 * 9 * 8 * 7 * 6!}{6! * 4 * 3 * 2 * 1}$

$^{10}C_4 = \frac{10 * 9 * 8 * 7 }{4 * 3 * 2 * 1}$

$^{10}C_4 = \frac{5040}{24}$

$^{10}C_4 = 210$

Ways of selecting both is calculated as follows

$Both = 3876 * 210$

$Both = 813960$