Question

A quad-core processor can handle 1 program on each of its 4 cores at the same time. If there are 20 programs queued to run on it, and each program can only be assigned to one core, how many different combinations of programs can be run at the same time*

Answer 1

Answer:

4845 different combinations of programs

Explanation:

A combination is an arrangement where order is NOT important.

In this case, the number of different combinations of assignments of the programs is,

$_^{20}C_{4} = \frac{20!}{4!(20-4)!}$

$_^{20}C_{4} = \frac{20.19.18.17.16!}{4.3.2.1(16)!}$

$_^{20}C_{4} = \frac{20.19.18.17}{4.3.2.1}$

$_^{20}C_{4} = \frac{116280}{24}=4845$

Hope this helps!