Of the 15-letter passwords formed by mixing • 4 upper-case letters, chosen from A to Z, allowing repeats, • 5 lower-case letters, chosen from a to z, without repeats, and • 6 numbers, chosen

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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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Of the 15-letter passwords formed by mixing
• 4 upper-case letters, chosen from A to Z, allowing repeats,
• 5 lower-case letters, chosen from a to z, without repeats, and
• 6 numbers, chosen from 1 to 9, without repeats,
I select one at random. Determine the following probabilities:

6. Of the 15-letter passwords formed by mixing
• 4 upper-case letters, chosen from A to Z, allowing repeats,
• 5 lower-case letters, chosen from a to z, without repeats, and
• 6 numbers, chosen from 1 to 9, without repeats,
I select one at random. Determine the following probabilities:
(a) Prob (my word includes no vowels)
(b) Prob (my word has no two numbers next to each other)
(c) Prob (my word begins with an upper-case vowel and ends with 9)
Leave your probabilities in terms of m", Pm, Cm, and factorials.
Transcribed Image Text:6. Of the 15-letter passwords formed by mixing • 4 upper-case letters, chosen from A to Z, allowing repeats, • 5 lower-case letters, chosen from a to z, without repeats, and • 6 numbers, chosen from 1 to 9, without repeats, I select one at random. Determine the following probabilities: (a) Prob (my word includes no vowels) (b) Prob (my word has no two numbers next to each other) (c) Prob (my word begins with an upper-case vowel and ends with 9) Leave your probabilities in terms of m", Pm, Cm, and factorials.
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