Question

wes has six errands to run (picking up the dry cleaning, going to the grocery store, getting gas, going to the bank, going to the library, and going to the video store). he only haves time to run 3 errands this afternoon. how many different combinations of three errands could he choose to run?

Answer 1

if you did 1*2*3*4*5*6 it's 720

Answer 2

Answer: 120 different combinations  .

Step-by-step explanation:

The combination of n things taking m things at a time is given by :-

$C(n,m)=\dfrac{n!}{m!(n-m)!}$

Given : The total numbers of errands = 6

Now, the combination of 6 errands taking 3 at a time is given by :-

$C(6,3)=\dfrac{6!}{3!(6-3)!}\\\\=\dfrac{6\times5\times4\times3!}{3!}=120$

Hence, he could choose to run 120 different combinations of three errands .