Evaluate the expression 5C2?

We have to evaluate the expression C5₂

Solution

To evaluate the expression C⁵₂ we use the following formula

nCr =n! / r! (n – r)!

n = 5
r = 2

Substitute n and r values in above formula

nCr =n! / r! (n – r)!

C⁵₂= 5! / 2! (5-2)!

C⁵₂= 5! / 2! (3)!

Find the factorial for 5!, 2! & 3!, substitute the corresponding values in the below expression and simplify.

= 5 X 4 X 3 X 2 X 1 / (2 X 1) ( 3 X 2 X 1)

= 120/ (2 ) (6)

= 120 / 12

= 10
C5₂= 10

Answer

C⁵₂= 10