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)
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. 

(a + b)° = 1
(a + b)! = 1a + 1b
%3D
(a + b)? = 1a? + 2ab + 1b?
%3D
(a + b)3 :
= 1a3 + 3a?b + 3ab? + 1b3
(a + b)* = 1a* + 4a°b + 6a?b? + 4ab³ + 1b*
%3D
(a + b)5 = 1a5+ 5a*b+ 10a b? + 10a?b3 + 5ab*+ 1b5
%3D
(a + b)6 = 1a° + 6ab + 15a*b? + 20a°b³ + 15 a²b* + 6ab5 + 1b6
%3D
(a + b) = 1a7 + 7a°b+ 21a b2 + 35a*b3 + 35a b*+ 21a b5 + 7ab6 + 1b7
%3D
(a + b)8 1a+ 8a'b+ 28a b2 + 56a*b3 +70a*b* +56a°b5+28a b +8ab7+ 1b8
Transcribed Image Text:(a + b)° = 1 (a + b)! = 1a + 1b %3D (a + b)? = 1a? + 2ab + 1b? %3D (a + b)3 : = 1a3 + 3a?b + 3ab? + 1b3 (a + b)* = 1a* + 4a°b + 6a?b? + 4ab³ + 1b* %3D (a + b)5 = 1a5+ 5a*b+ 10a b? + 10a?b3 + 5ab*+ 1b5 %3D (a + b)6 = 1a° + 6ab + 15a*b? + 20a°b³ + 15 a²b* + 6ab5 + 1b6 %3D (a + b) = 1a7 + 7a°b+ 21a b2 + 35a*b3 + 35a b*+ 21a b5 + 7ab6 + 1b7 %3D (a + b)8 1a+ 8a'b+ 28a b2 + 56a*b3 +70a*b* +56a°b5+28a b +8ab7+ 1b8
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