Use any method described in this section to solve each...

Name: Problem 71, Chapter 7: Student's Solutions Manual for College Algebra
Uploaded: 2021-07-08T03:32:27-08:00
Duration: 3 min 56 s
Channel: Rebecca Johnson
Description: Use any method described in this section to solve each problem. See Examples 1–9. Combination Lock A briefcase has 2 locks. The combination to each lock consists of a 3 -digit number, where digits may be repeated. How many combinations are possible? (Hint: The word combination is a misnomer. Lock combinations are permutations where the arrangement of the numbers is important.)

Use any method described in this section to solve each problem. See Examples 1–9. Combination Lock A briefcase has 2 locks. The combination to each lock consists of a 3 -digit number, where digits may be repeated. How many combinations are possible? (Hint: The word combination is a misnomer. Lock combinations are permutations where the arrangement of the numbers is important.)

Use any method described in this section to solve each problem. See Examples 1–9.
Combination Lock A briefcase has 2 locks. The combination to each lock consists of a 3 -digit number, where digits may be repeated. How many combinations are possible? (Hint: The word combination is a misnomer. Lock combinations are permutations where the arrangement of the numbers is important.)

Key Concepts

Permutations with Repetition

Permutations refer to arrangements where the order of items is important. In cases where repetition is allowed, each position in the arrangement can be filled independently from the same set of choices, leading to a total number of arrangements equal to the number of choices raised to the power of the number of positions. This concept is key in problems where the order matters even though the term 'combination' might be used in casual language.

Fundamental Counting Principle

This principle states that if there are several tasks to be performed in sequence and each task can be done in a certain number of ways independently of the others, then the total number of ways to complete all tasks is the product of the number of ways to do each individual task. It is a basic approach for calculating the number of outcomes in multi-stage problems.

Transcript

00:02 Hi guys.

00:04 We are going to go over the basics of counting theory, and i try to approach these problems the same, whether we're talking about permutation, combinations, or just your fundamental counting principles.

00:18 In this case, we have a briefcase that has two locks, and each lock has a combination of a three -digit number.

00:29 So this is just our fundamental counting principles.

00:34 If it was a combination, it would mean that i'm not using all of my numbers.

00:41 Like, if you're going to do something that's a combination, you'd have like three out of five numbers or something like that.

00:50 This word combination here is misleading.

00:54 This is talking about a combination lock.

00:58 It's not describing the type of counting theory.

01:03 It's just describing the lock.

01:06 So i have two combination locks.

01:09 Each one has three digits.

01:12 So there's one and there's the second.

01:16 The digits that we have to choose from go from one to nine.

01:27 Any one of these digits could be used for the first number in my combination.

01:33 So altogether i have 10 digits.

01:38 Oh, that's 9.

01:39 Guess what i'm missing? how about the zero? there we go.

01:43 Now i have my 10 digits.

01:47 The part we need to look at now is whether the problem says the digits can be repeated or if they can't be repeated.

02:03 They can or can't be repeated.

02:06 If they can't be repeated, then that means whatever...

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