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Chapter 11: Problem 11

Use the formula for \({ }_{n} C_{r}\) to evaluate each expression. \({ }_{8} C_{1}\)

Short Answer

Expert verified
The result of evaluating \({ }_{8} C_{1}\) is 8.

Step by step solution

01

Apply the formula

First, apply the combination formula \({ }_{n} C_{r} = \frac{n!}{r!(n-r)!}\) where n! is shorthand for the factorial of n, r! is the factorial of r and (n-r)! is the factorial of the difference between n and r. In this case, substitute n = 8 and r = 1.
02

Calculate the factorials

Next, compute the various factorials needed for the formula. Factorial means multiplying the number by all positive integers less than it. Here, we compute 8! (i.e., 8*7*6*5*4*3*2*1 = 40320), 1! (1), and (8-1)! (i.e., 7*6*5*4*3*2*1 = 5040).
03

Evaluate the combination

Finally, substitute the factorial values back into the combination formula and simplify: \({ }_{8} C_{1}=\frac{40320}{1*5040}\). Simplifying gives the final answer as 8.

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Most popular questions from this chapter

We return to our box of chocolates. There are 30 chocolates in the box, all identically shaped. Five are filled with coconut, 10 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a coconut-filled chocolate followed by a solid chocolate.

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