How do u expand (20 c 7) to

Question

make it equal to 77, 520?

Answer 1

Combinations formula n c r = n! / r! (n - r)!

Substitute n = 20 and r  = 7 in the above formula

20 C 7 = 20! / 7!(20 - 7)! = 20! / 7!(13!)

                                           = 14×15×16×17×18×19×20 / 1×2×3×4×5×6×7

Simplify

                                           = 77520.