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Chapter 11: Problem 9

Use the formula for \({ }_{n} C_{r}\) to evaluate each expression. \({ }_{11} C_{4}\)

Short Answer

Expert verified
The expression \({ }_{11} C_{4}\) simplifies to 330.

Step by step solution

01

Identify the values for n and r

From the statement of the problem, it can be seen that n = 11 and r = 4.
02

Evaluate Factorials

The factorial of a number is the product of all positive integers less than or equal to that number. So, 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Similarly, 4! = 4 x 3 x 2 x 1, and (11-4)! = 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1.
03

Substitute into the formula

Substitute the values and the factorials into the combination formula: \(_{11} C_{4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4!7!}.\) There may be some numbers in the factorial expressions that can cancel out.
04

Simplify the expression

Simplify the expression by cancelling out the common terms in the numerator and denominator. This leads to a simplified result of 330.

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