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Chapter 5: Q 5.162. (page 242)

Evaluate the following binomial coefficients.

a.53b.100c.1010d.95

Short Answer

Expert verified

Part (a) 10

Part (b) 1

Part (c) 1

Part (d) 126

Step by step solution

01

Part (a) Step 1. Given information.

The given binomial coefficient is:

53

02

Part (a) Step 2. Evaluate the binomial coefficient.

53=5!3!脳5-3!=5!3!脳2!=5脳41脳2=10

03

Part (b) Step 1. Evaluate the binomial coefficient 100.

100=10!0!脳10-0!=10!0!脳10!=10!1脳10!=1

04

Part (c) Step 1. Evaluate the binomial coefficient 1010.

1010=10!10!脳10-10!=10!10!脳0!=10!10!脳1=1

05

Part (d) Step 1. Evaluate the binomial coefficient 95.

95=9!5!脳9-5!=9!5!脳4!=9脳8脳7脳61脳2脳3脳4=126

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