How do you evaluate 5C2 + 5C1?

We have to evaluate the expression 5C2 + 5C1

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

To evaluate the expression C⁵¹ we use the following formula

nCr =n! / r! (n – r)!

n = 5
r = 1

Substitute n and r values in above formula

nCr =n! / r! (n – r)!

C⁵²= 5! / 1! (5-1)!

C⁵²= 5! / 1! (4)!

Find the factorial for 5!, 1! & 4!, substitute the corresponding values in the below expression and simplify.

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

= 120/ (24)

= 120 / 24

= 5
C51= 5

5C2 + 5C1 = 10 + 5 = 15