Question

Evaluate 12C3 Please show your work - Thank you!

Answer 1

Answer: 220

Step-by-step explanation:

We know that the combination is a method to determine the total outcomes of an event where order of the outcomes does not matter.

To calculate combinations, we apply the formula given below:-

$^nC_r = \dfrac{n!}{(n-r)!r!}$, where n represents the total number of items, and r represents the number of things being chosen at a time.

The given expression : $^{12}C_3$

Then by using above formula , we have

$^{12}C_3 = \dfrac{12!}{(12-3)!3!}\\\\=\dfrac{12\times11\times10\times9!}{9!\times6}=220$

Answer 2

12C3 means nCr
You have 12 items of which you want to choose 3 and the order in which you choose them does not matter.


n!                 12!                  12!          479001600
----------  =  --------           = -------  =  ----------------- = 220
(r!(n-r)!      3!(12-3)!            3!(9!)         21177280