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Chapter 11: Problem 10

Use the formula for \({ }_{n} C_{r}\) to evaluate each expression. \({ }_{12} C_{5}\)

Short Answer

Expert verified
The result of \({ }_{12} C_{5}\) is 792.

Step by step solution

01

Identify n, r values

In the expression \({ }_{12} C_{5}\), 'n' is 12 and 'r' is 5. So these values need to be plugged into the formula.
02

Calculate Factorials

Factorial of n, r and (n-r) need to be calculated. Factorial (n!) of a non-negative integer n is the product of all positive integers less than or equal to n. So, calculate 12!, 5! and (12-5)!, which are 479001600, 120 and 5040 respectively.
03

Substitute in the Formula

Substitute the calculated values into the formula: \({ }_{12} C_{5} = \frac{12!}{5!(12-5)!} = \frac{479001600}{120*5040}\)
04

Calculate the Result

Calculate the value of the expression. The result comes out to be 792.

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