Question

Can someone break this down for me!! I'm stuck

Answer 1

Answer:

$_{12}C_9=220$

Step-by-step explanation:

Recall the definition for the combination symbol with the use of factorial (symbol !):

$_nC_k=\frac{n!}{k!(n-k)!}$

Therefore, for the case where n = 12 and k = 9, we have:

$_{12}C_9=\frac{12!}{9!(3)!}\\_{12}C_9=\frac{12*11*10*9*8*7*6*5*4*3*2}{9*8*7*6*5*4*3*2(3*2)}\\\\_{12}C_9=\frac{12*11*10}{3*2}\\\\_{12}C_9=\frac{1320}{6}\\\\_{12}C_9=220$