(a) To log on to a certain computer account, the user must type in a 4 -letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4 -letter passwords are possible? (There are 26 letters in the alphabet.) (b) A certain committee consists of 15 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.

(a) To log on to a certain computer account, the user must type in a 4 -letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4 -letter passwords are possible? (There are 26 letters in the alphabet.) (b) A certain committee consists of 15 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.

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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Question

(a) To log on to a certain computer account, the user must type in a

-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such

-letter passwords are possible? (There are

letters in the alphabet.)

(b) A certain committee consists of

people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these

offices be filled? Assume that a committee member can hold at most one of these offices.

Expert Solution

Step 1: Define the initial Variables and find 'a'

The number of letters password that user must type = 4

As given,

No letters may be repeated.

Only the lower case letters may be used.

Total number of letters = 26

The number of 4-letter passwords are possible are,

= 26*25*24*23

= 358800

Step by step

Solved in 3 steps

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