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Chapter 12: Q. 12.68. (page 1208)

Evaluate each binomial coefficient,

a21b1111c96d65

Short Answer

Expert verified

Evaluated form of each binomial coefficient,

a2b1c84d6

Step by step solution

01

Part (a) Step 1. Evaluate the binomial by using the formula.

Use the definition of a binomial coefficient,

nr=n!r!n-r!

Use this formula to solve the given coefficient.

21=2!1!2-1!=2!1!1!=2脳11脳1=2

02

Part (b) Step 1. Evaluate the binomial by using the formula.

Use the formula to solve the given coefficient.

1111=11!11!11-11!=11!11!0!=11!11!1=11!11!=1

03

Part (c) Step 1. Evaluate the binomial by using the formula.

Use the formula to solve the given coefficient.

96=9!6!9-6!=9!6!3!=9脳8脳7脳6!6!脳3脳2脳1=9脳8脳73脳2脳1=84

04

Part (d) Step 1. Evaluate the binomial by using the formula.

Use the formula to solve the given coefficient.

65=6!5!6-5!=6!5!1!=6脳5脳4脳3脳2脳15脳4脳3脳2脳1=6

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Most popular questions from this chapter

Find the sum of the first 30 terms of the arithmetic sequence: 5, 9, 13, 17, 21, 鈥�.

Find the coefficient of the x4 term of (x+2)7.

Determine if each sequence is arithmetic. If so, indicate the common difference.

(a)鈭�4,4,2,10,8,16,鈥�(b)鈭�3,鈭�1,1,3,5,7,鈥�(c)7,2,鈭�3,鈭�8,鈭�13,鈭�18,鈥�

Find the eleventh term of the sequence 7,14,28,56,112,224,鈥�Then find the general term for the sequence.

In the following exercises, expand each binomial using Pascal's Triangle.

(a+b)8
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