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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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Transcribed Image Text:There are 6' possible outcomes for the seven dice. If each of the six numbers is to appear at least once
among the seven dice, then one number must appear twice and each of the other five numbers must
appear once. Suppose first that the number 1 appears twice and each of the other numbers appears
once. The number of outcomes of this type in the sample space is equal to the number of different
7!
arrangements of the symbols 1, 1, 2, 3, 4, 5, 6, which is
2!(1!)5
7!
There is an equal number of
2
outcomes for each of the other five numbers which might appear twice among the seven dice. Therefore,
the total number of outcomes in which each number appears at least once is
6(7!)
and the probability
of this event is
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