What is the value of 10C7?

A. 12

B. 720

C. 5040

D. 604,800

The answer is 120

For combinations we use:

nCr = n! / (r! (n-r) !)

10C7 = ?

n = 10

r = 7

10C7 = 10! / (7! (10-7) !)

= (10*9*8*7*6*5*4*3*2*1) / (7*6*5*4*3*2*1*3!)

= 3628800 / (5040 * 3*2*1)

= 3628800/30240

= 120