How do you evaluate 9C3?

We have to evaluate the expression 9C3

Solution

To evaluate the expression 9C3 we use the following formula

nCr =n! / r! (n – r)!

n = 9
r = 3

Substitute n and r values in above formula

nCr =n! / 3! (n – r)!

9C3= 9! / 3! (9-3)!

9C3= 9! / 3! (6)!

Find the factorial for 9!, 3! & 6!, substitute the corresponding values in the below expression and simplify.

= 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 / (3 X2 X 1) (6 X 5 X 4 X3 X 2 X 1)

=362880/ (6 ) (720)

= 362880 / 4320

= 84
9C3= 84

Answer

9C3= 84

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