/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1100 Two cards are to be drawn in ord... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 34: Problem 1100

Two cards are to be drawn in order from a pack of 4 cards (say, an ace, king, queen, and jack), the drawn card not being replaced before the second card is drawn. How many different drawings are possible?

Short Answer

Expert verified
There are 12 different ways to draw 2 cards in a specific order from a pack of 4 cards without replacement, using the formula for permutations: \(4P2 = \frac{4!}{(4-2)!} = \frac{24}{2} = 12\).

Step by step solution

01

Analyze the given problem

We are given a pack of 4 cards: ace, king, queen, and jack. We need to find the total number of ways to draw 2 cards from this pack in a specific order, without replacement. Since the order matters and there is no replacement, we can use permutations to solve this problem.
02

Use the formula for permutations

The formula for permutations is: \[ nPr = \frac{n!}{(n-r)!} \] Where 'n' represents the total number of objects and 'r' represents the number of objects you want to choose from 'n' objects in a particular order, the exclamation point, "!", indicates a factorial function. In our case, we have 4 cards to choose from (n=4) and we want to draw 2 cards (r=2). So, we have to find 4P2 using the formula.
03

Calculate the permutation

Now, we'll calculate the permutation using the formula: \[ 4P2 = \frac{4!}{(4-2)!} \] First, we need to find the factorials of 4 and 2: 4! = 4 x 3 x 2 x 1 = 24 2! = 2 x 1 = 2 Now, plug the factorial values into the formula: \[ 4P2 = \frac{24}{2} \]
04

Final calculation

Now, divide 24 by 2 to get the final answer: \[ 4P2 = \frac{24}{2} = 12 \] So, there are 12 different ways to draw 2 cards in a specific order from a pack of 4 cards without replacement.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Evaluate each of the following symbols: (a) \(\mathrm{C}(6,3)\) (b) \(\mathrm{C}(18,16)\)

In how many ways can 5 prizes be given away to 4 boys, when each boy is eligible for all the prizes?

Find \({ }_{9} \mathrm{C}_{4}\).

A lady has 12 friends. She wishes to invite 3 of them to a bridge party. How many times can she entertain without having the same 3 people again?

A manufacturer produces 7 different items. He packages assortments of equal parts of 3 different items. How many different assortments can be packaged?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.