Lesson Simple and simplest problems on permutations
Algebra
->
Permutations
-> Lesson Simple and simplest problems on permutations
Log On
Algebra: Combinatorics and Permutations
Section
Solvers
Solvers
Lessons
Lessons
Answers archive
Answers
Source code of 'Simple and simplest problems on permutations'
This Lesson (Simple and simplest problems on permutations)
was created by by
ikleyn(52908)
:
View Source
,
Show
About ikleyn
:
<H2>Simple and simplest problems on permutations</H2> This lesson is the continuation of the lesson <A HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson?content_action=show_dev>Introduction to Permutations</A>, which is under the current topic in this site. The lesson contains some typical word problems on <B>permutations</B> in addition to that are placed in the previous lesson. <H3>Problem 1</H3> A company produces flags that are sewed of 5 differently colored horizontal strips each of the blue, red, yellow, white and green color with no repeating colors. How many differently colored patterns are there for these flags? <B>Solution</B> <pre> Each colored pattern is the permutation of 5 differently colored non-repeating horizontal strips in positions from 1 to 5 counted from top to bottom. The total number of such permutations is 5! = 1*2*3*4*5 = 120. So, there are 120 differently colored patterns for these flags. </pre> <H3>Problem 2</H3>How many ways are there to put pennies, nickels, dimes and quarters in 4 different boxes in such a manner that every box contains the coins of the same unique value? <B>Solution</B> <pre> Each arrangement of the values of coins between four boxes is the permutation of four items. The total number of such permutations is 4! = 1*2*3*4 = 24. So, there are 24 ways to arrange the boxes and the values of coins. </pre> <H3>Problem 3</H3>In how many ways six different shortcut icons could be ordered in a line on the computer screen? <B>Solution</B> <pre> Each ordering of the 6 different shortcut icons in a line on the computer screen is the permutation of six items. The total number of such permutations is 6! = 1*2*3*4*5*6 = 720. So, there are 720 ways to order 6 different shortcut icons in a line on the computer screen. </pre> <H3>Problem 4</H3>In how many ways can 19 boys and 2 girls be arranged in sequence ? <B>Solution</B> <pre> In all, there are 21 = 19+2 persons to be arranged in sequence. Anyone of 21 persons can be placed in the 1-st position. Anyone of the 20 remaining persons can be placed in the 2-nd position. Anyone of the 19 remaining persons can be placed in the 3-rd position. . . . and so on . . . In all, there are 21! arrangements. </pre> My lessons on Permutations and Combinations in this site are - <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A> - <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A> - Simple and simplest problems on permutations (this lesson) - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Special-type-permutations-problems.lesson>Special type permutations problems</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/How-many-different-permutations-may-exist-ubder-given-restrictions.lesson>Problems on Permutations with restrictions</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Math-circle-level-problem-on-Permutations.lesson>Math circle level problem on Permutations</A> - <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A> - <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A> - <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Combinations-problems-with-restrictions.lesson>Problems on Combinations with restrictions</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Math-circle-level-problem-on-Combinations.lesson>Math circle level problem on Combinations</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Arranging-elements-of-sets-containing-undistinguishable-elements.lesson>Arranging elements of sets containing indistinguishable elements</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Persons-sitting-around-a-circular-table.lesson>Persons sitting around a circular table</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Combinatoric-problems-for-entities-other-than-permutations-and-combinations.lesson>Combinatoric problems for entities other than permutations and combinations</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Fundamental-counting-principle-problems.lesson>Fundamental counting principle problems</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Miscellaneous-problems-on-permutations-combinations-and-other-combinatoric-entities.lesson>Miscellaneous problems on permutations, combinations and other combinatoric entities</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Some-twisted-combinatorics-problem.lesson>Some twisted combinatorics problem</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Inclusion-Exclusion-principle.lesson>Inclusion-Exclusion principle problems</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/DERANGEMENT-problems.lesson>Derangement problems</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/In-how-many-ways-N-distinguishable-objects--can-be-distributed-among-n-different-boxes.lesson>In how many ways N distinguishable objects can be distributed among n different boxes ?</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Stars-and-bars-method-for-Combinatorics-problems-2.lesson>Stars and bars method for Combinatorics problems</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Men-and-women-standing-in-line-.lesson>Men and women standing in line</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/One-combinatorial-Geometry-problem-solved-using-the-Euler-formula.lesson>One combinatorial Geometry problem solved using the Euler formula</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/Nice-recreational-problems-on-permutations.lesson>Nice recreational problems on permutations</A> - <A HREF =https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-II.
