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Say a family was to want 8 kids and were hoping for the probability of 6 girls and 2 boys. Which of the terms in pascals binomial expression for (a+b)^8 would be used for your calculations? Explain. An attached picture of the  (a+b)^8 row is attached below.

Say a family was to want 8 kids and were hoping for the probability of 6 girls and 2 boys. Which of the terms in pascals binomial expression for (a+b)^8 would be used for your calculations? Explain. An attached picture of the  (a+b)^8 row is attached below.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Say a family was to want 8 kids and were hoping for the probability of 6 girls and 2 boys. Which of the terms in pascals binomial expression for (a+b)^8 would be used for your calculations? Explain.

An attached picture of the  (a+b)^8 row is attached below. 

The image displays the Binomial Theorem used to expand powers of a binomial expression \((a+b)^n\). 1. \((a+b)^0 = 1\) 2. \((a+b)^1 = 1a + 1b\) 3. \((a+b)^2 = 1a^2 + 2ab + 1b^2\) 4. \((a+b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3\) 5. \((a+b)^4 = 1a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + 1b^4\) 6. \((a+b)^5 = 1a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + 1b^5\) 7. \((a+b)^6 = 1a^6 + 6a^5b + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6ab^5 + 1b^6\) 8. \((a+b)^7 = 1a^7 + 7a^6b + 21a^5b^2 + 35a^4b^3 + 35a^3b^4 + 21a^2b^5 + 7ab^6 + 1b^7\) 9. \((a+b)^8 = 1a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a^3b^5 + 28a^2b^6 + 8ab^7 + 1b^8\) These expansions follow the pattern dictated by Binomial coefficients, which correspond to the entries in Pascal's Triangle. Each line represents the expansion of a binomial to an increasing power from 0 to 8. The coefficients of the terms in each expansion align with the rows of Pascal's Triangle.
Transcribed Image Text:The image displays the Binomial Theorem used to expand powers of a binomial expression \((a+b)^n\). 1. \((a+b)^0 = 1\) 2. \((a+b)^1 = 1a + 1b\) 3. \((a+b)^2 = 1a^2 + 2ab + 1b^2\) 4. \((a+b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3\) 5. \((a+b)^4 = 1a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + 1b^4\) 6. \((a+b)^5 = 1a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + 1b^5\) 7. \((a+b)^6 = 1a^6 + 6a^5b + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6ab^5 + 1b^6\) 8. \((a+b)^7 = 1a^7 + 7a^6b + 21a^5b^2 + 35a^4b^3 + 35a^3b^4 + 21a^2b^5 + 7ab^6 + 1b^7\) 9. \((a+b)^8 = 1a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a^3b^5 + 28a^2b^6 + 8ab^7 + 1b^8\) These expansions follow the pattern dictated by Binomial coefficients, which correspond to the entries in Pascal's Triangle. Each line represents the expansion of a binomial to an increasing power from 0 to 8. The coefficients of the terms in each expansion align with the rows of Pascal's Triangle.
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