1. It's intended to have numbers with 8 figures but using only the figures 1, 2, 3 and 4. 1.1) How many numbers can we have? 1.2) How many numbers can we have in a way that the figure 1 appears exactly 3 times and the figure 2 appears exactly 2 times? 1.3) How many numbers can we have in a way that each of the figures 1, 2, 3 and 4 appears at least once?

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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1. It's intended to have numbers with 8 figures but using only the figures 1, 2, 3 and 4.
1.1) How many numbers can we have?
1.2) How many numbers can we have in a way that the figure 1 appears exactly 3 times
and the figure 2 appears exactly 2 times?
1.3) How many numbers can we have in a way that each of the figures 1, 2, 3 and 4
appears at least once?
Transcribed Image Text:1. It's intended to have numbers with 8 figures but using only the figures 1, 2, 3 and 4. 1.1) How many numbers can we have? 1.2) How many numbers can we have in a way that the figure 1 appears exactly 3 times and the figure 2 appears exactly 2 times? 1.3) How many numbers can we have in a way that each of the figures 1, 2, 3 and 4 appears at least once?
Expert Solution
Step 1

In these kind of questions we will use laws of permutations and combinations. In the first option we can use any figure any number of times we wish to therefore every digit will have 4 options of figures to use to.

In second option 1 appears 3 times and 2 appears two times this means 5 digits of our figures are reserved and we can use any digit for only rest of 3 digits. While we will be have 8C3 number of ways of choosing places of those three 1's and 8Cfor two digit 2.

In third option the four places are reserved for 4 digits rest can be filled by any digit.

 

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