There are 4 boys and 6 girls that are going to be seated in a row. Let’s say a boy is sandwiched between two girls to mean the boy has a girl immediately to his left and to his right. If the ten children are labeled b1, b2, b3, b4, g1, g2, g3, g4, g5, g6 then the seating arrangement g1, b1, b2, g2, b3, g4, g5, b4, g6 has 2 boys sandwiched between 2 girls (b3 and b4) whereas the arrangement g1, b1, g2, b2, g3, b3, g4, b4, g5, g6 has all 4 boys sandwiched. Compute the expected number of these 4 boys that are sandwiched between two girls.

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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There are 4 boys and 6 girls that are going to be seated in a row. Let’s say a boy is sandwiched between two girls to mean the boy has a girl immediately to his left and to his right. If the ten children are labeled b1, b2, b3, b4, g1, g2, g3, g4, g5, g6 then the seating arrangement

g1, b1, b2, g2, b3, g4, g5, b4, g6

has 2 boys sandwiched between 2 girls (b3 and b4) whereas the arrangement

g1, b1, g2, b2, g3, b3, g4, b4, g5, g6

has all 4 boys sandwiched.

Compute the expected number of these 4 boys that are sandwiched between two girls.

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