What is the probability that on the 25th roll of a die, face 4 occurs for the 5th time?

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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What is the probability that on the 25th roll of a die, face 4 occurs for the 5th time?

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Probability is defined as the sum of favorable ways of an events divided by the total number of ways.

Permutations and combinations:

When one has to choose among a set of objects or people, then combination is used to find the number of ways. The order in which they are chosen does not matter here.

On the other hand, if one has to find the number of ways of arranging certain objects, then arrangement is used. Here, the order always matter.

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