/*! 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 50 In how many distinct ways can th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 50

In how many distinct ways can the letters of the word SCIENCE be arranged?

Short Answer

Expert verified
The total number of distinct arrangements of the word 'SCIENCE' is 1,260.

Step by step solution

01

Calculation of permutations

First, calculate the total number of permutations without considering the repetitions. The word SCIENCE contains 7 letters, so without considering the repetitions, the total number of arrangements would be 7!, which stands for factorial of 7.
02

Handling repetitions

Now, consider the repetitions. The letters 'E' and 'C' each repeat twice in the word. So, the total number of these duplicate arrangements should be divided from the total arrangements. This gives us 7! divided by 2! (for 'E') and again divided by 2! (for 'C').
03

Final calculation

Now you just need to do the calculations. The factorial of a number is the product of all positive integers less than or equal to that number. Thus, calculate 7! / (2! * 2!)

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

You are taking a multiple-choice test that has five questions. Each of the questions has three answer choices, with one correct answer per question. If you select one of these three choices for each question and leave nothing blank, in how many ways can you answer the questions?

A social security number contains nine digits, such as 074-66-7795. How many different social security numbers can be formed?

Involve computing expected values in games of chance. The spinner on a wheel of fortune can land with an equal chance on any one of ten regions. Three regions are red, four are blue, two are yellow, and one is green. A player wins \(\$ 4\) if the spinner stops on red and \(\$ 2\) if it stops on green. The player loses \(\$ 2\) if it stops on blue and \(\$ 3\) if it stops on yellow. What is the expected value? What does this mean if the game is played ten times?

Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. My expected value in a state lottery game is \(\$ 7.50\).

Write an original problem that can be solved using the Fundamental Counting Principle. Then solve the problem.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.