1. An optometry clinic's office is instituting a new system for patient identification numbers. Under the new system, each username must be exactly 6 characters long; available characters are either uppercase or lowercase letters (A-Z or a-z, 52 possible choices) and numerical digits (0-9, 10 possible choices). The clinic's office would like the first character being uppercase letter, the last three characters to be numerical digits, and the middle two characters to be lowercase letter. (a) How many different ID are possible (assume letters and numbers can be chosen more than once)? (b) How many different ID are possible if none of the numerical digits can be used more than once? (c) How many different ID are possible if no character (letters or numbers) can be used more than once?

1. An optometry clinic's office is instituting a new system for patient identification numbers. Under the new system, each username must be exactly 6 characters long; available characters are either uppercase or lowercase letters (A-Z or a-z, 52 possible choices) and numerical digits (0-9, 10 possible choices). The clinic's office would like the first character being uppercase letter, the last three characters to be numerical digits, and the middle two characters to be lowercase letter. (a) How many different ID are possible (assume letters and numbers can be chosen more than once)? (b) How many different ID are possible if none of the numerical digits can be used more than once? (c) How many different ID are possible if no character (letters or numbers) can be used more than once?

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Description: 1. An optometry clinic's office is instituting a new system for patient identification numbers. Under thenew system, each username must be exactly 6 characters long; available characters are either uppercaseor lowercase letters (A-Z or a-z, 52 possi

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

Topic Video

Question

1. An optometry clinic's office is instituting a new system for patient identification numbers. Under the
new system, each username must be exactly 6 characters long; available characters are either uppercase
or lowercase letters (A-Z or a-z, 52 possible choices) and numerical digits (0-9, 10 possible choices).
The clinic's office would like the first character being uppercase letter, the last three characters to be
numerical digits, and the middle two characters to be lowercase letter.
(a) How many different ID are possible (assume letters and numbers can be chosen more than once)?
(b) How many different ID are possible if none of the numerical digits can be used more than once?
(c) How many different ID are possible if no character (letters or numbers) can be used more than
once?
(d) You are one of the clinic's patients, but you have forgotten your ID when you go to see the op-
tometrist. You don't remember the whole username, but you do remember that the first two
characters are "Lo."
Using this information you take a guess. What is the probability that you guess correctly? Note:
the only restrictions are those from the original problem, not any previous sub-problems.

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