Question

a box contains 12 pencils of distinct colors. how many different sets of 5 pencils can be chosen from it?

Answer 1

Since we need to choose 5 pencils from 12 colors, then we will use the combination

`^nC_r`

Where

n = 12

r = 5

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

Substitute n by 12 and 4 by 5 in the rule

`^(12)C_5=(12!)/((12-5)!\cdot5!)`

We will simplify it

`\begin{gathered} ^(12)C_5=(12*11*10*9*8*7*6*5*4*3*2*1)/((7*6*5*4*3*2*1)\cdot(5*4*3*2*1)) \\ \\ ^(12)C_5=792 \end{gathered}`

There are 792 sets of pencils