77-80 - Binomial Expansion Expand the expression.77. (А — В)78. (x + 2)579. (1 — х')680. (2x + y)*

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College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Sequences And Series

Section: Chapter Questions

Problem 79E

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Using the binomial theorem, evaluate (2x+y)n either directly or first by expanding it as (x + (x + y))n and then expanding out the (x + y) terms. Collecting like terms on either side and comparing coefficients, you should obtain an identity involving sums of binomial coefficients. Give an independent combinatorial proof of this identity.
4 Suppose we have 3000 identical sheets separated into packs of 25 sheets each. Use generating functions to calculate the number of ways in which you can distribute the packs of 25 sheets among four groups of students so that each group has at least 150 sheets and more than 1000 sheets. Express your answer using binomial coefficients and include the calculations made. Explain your solution in detail.
In the expansion of a binomial the third term is equal to , the fourth term is , and the binomial coefficients of the third and the sixth term are equal. Find the values of , , and . Clear question attached
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Serial numbers for a product are made using 3 letters followed by 2 numbers. If the letters are taken from the first 8 letters of the alphabet with no repeats and the numbers are taken from the 10 digits (0 − 9) with no repeats, how many serial numbers are possible?
Serial number for a product are to be made using 4 letters followed by 2 digits. The letters are to be taken from the first 9 letters of the alphabet, with no repeats. The digits are taken from the 10 digits are taken from the 10 digits(0,1,2,...,9),with no repeats. How many serial numbers can be generated?
Serial numbers for a product are to be made using 4 letters followed by 2 digits. The letters are to be taken from the first 9 letters of the alphabet, with no repeats. The digits are taken from the 10 digits (0,1,2,...,9), with no repeats. How many serial numbers can be generated?
Serial numbers for a product are to be made using 4 letters followed by 2 digits.The letters are to be taken from the first 9 letters of the alphabet, with no repeats.The digits are taken from the 10 digits (0, 1, 2,...,9), with no repeats.How many serial number can be generated?
A model for the number of lobsters caught per year is based on the assumption that the number of lobsters caught in a year is the average of the number caught in the two previous years. 1. Find a recurrence relation for {Ln}, where Ln is the number of lobsters caught in year n, under the assumption for this model. 2. Find Ln if 100,000 lobsters were caught in year 1 and 300,000 were caught in year 2.
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Binomial Thereom Expand the expression: (3x+2)^5=

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77-80 - Binomial Expansion Expand the expression. 77. (А — В) 78. (x + 2)5 79. (1 — х')6 80. (2x + y)*