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 TOPICS This page:   permutations/combinations    Search   Dr. Math See also the Dr. Math FAQ:   permutations and   combinations Internet Library:   permutations/combinations HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Permutations/Combinations Stars indicate particularly interesting answers or good places to begin browsing. Choose Three People from Five [05/09/2001] What do the fractions in the numerator and denominator mean? Where does the formula come from? Choosing Computer Disks [12/01/2001] A bin of computer disks contains a supply of disks from four different manufacturers. In how many ways can you choose 6 disks from the bin? Combinations of Images on a TV Screen [12/6/1995] I'd like to know how many images would be possible on a hypothetical TV screen. Combinations of the Letters in a Name [03/04/1998] A formula for the number of combinations of the letters in a name, however many times one letter appears in that name. Combinatorics Basics [07/07/1997] I need to prove that n chooses n-1 = n; e.g. C(n,n-1) = n. Committee of Six [10/07/1999] A club has 8 male and 8 female members and is choosing a committee of 6 members, 3 male and 3 female. How many different committees can be chosen? Counting Answer Keys [05/25/2001] A multiple-choice test has 30 questions, each with five choices. How many answer keys are possible? From Rock-Paper-Scissors to Stars and Bars [06/17/2014] An adult struggles to calculate multi-player Roshambo outcomes without explicitly enumerating clenched fists, open palms, and two fingers. Doctor Ian explains why neither permutations nor combinations applies to such a scenario of replacement without regard to order; Doctor Peterson introduces a new approach. Handshakes and Polygon Diagonals [09/12/2001] If a polygon has 42 sides, how many diagonals does it have? Math Symbol for C [12/15/1997] I am puzzled by one symbol of typing math. What does the upper case letter C mean? As in (2C1) (3C1) / (47C2) = 6/1081. Number and Letter Combinations [07/29/1997] How many possible combinations can a person make with the letters a-z and 1-9 starting from 1 digit and ending up with up to 8 digits? Number of Combinations for 7 Dice [2/22/1995] I'm looking for the derived formula solution for the following problem someone posted in a math echo: There are seven dice. Each die has six faces. How many different combinations are there of these seven dice? Number of Possible Telephone Numbers [7/15/1996] How many phone numbers are there given the following restrictions on certain digits of the number....? Number of Squares in an NxN Square [7/29/1996] How many squares are there in an 8 x 8 square? How many rectangles are there? Odds vs. Probability [12/06/1996] What's the probability that a man can draw the numbers 2 and 7 from a hat containing the numbers 1-8? Pascal's Triangle and Binomial Coefficients [09/11/2001] Why are Pascal's triangle and the binomial coefficients the same? Pascal's Triangle and the Tower of Hanoi [08/07/1997] There's a connection between Pascal's Triangle and the Tower of Hanoi game but I can't remember what it is! Permutations and Combinations: Deriving Formulae [06/18/1998] I have been trying to figure out how to arrive at the formula for calculating combinations. Possible Letter Arrangements [07/05/2000] Is there a formula I can use to quickly get the number of possible arrangements of five, six,or seven different letters? Powerball Lottery: Odds of Winning a Prize [09/02/2001] How are the Powerball lottery odds established? Rank of the Word FOCUS [06/27/2003] The letters 'CFOSU' are arranged in dictionary order. What is the rank of the word 'FOCUS' in this order? Round Robin Tournament Schedule [03/31/2000] Is there a systematic way to come up with a schedule for a round robin tournament for up to 32 teams, where each team plays every other team once? Squares in Rectangle Formula [06/30/2003] What is the equation for the number of squares in a rectangle (like the chessboard puzzle)? Ways To List 1, 2, ... 10 Out of Order [02/25/1997] How many ways are there to list the numbers one through ten so that no number appears in its own position (i.e. 1 is not first in the list, 2 is not second...)? 20 Golf Players [04/11/1997] How do you set up four teams such that the variance in the average team handicap is no more than one or two? Algorithm for Derangements [01/11/2003] I have been looking for a recursive algorithm to find all possible derangements of a set n. Analyzing Prime Factors [06/14/2007] Is there a number that has only three prime divisors (3, 5, and 7) and that has a total of 18 divisors? Arrangement [07/12/1999] How can I reduce the number of arrangements of the word ARRANGEMENT by using the probability of an occurrence? Arrangements of 0's, 1's, and 2's [03/14/2002] How many arrangements of six 0's, five 1's, and four 2's are there in which i) the first 0 precedes the first 1? ii) the first 0 precedes the first 1, precedes the first 2? Arrangements of Letters [09/14/1999] In how many ways can the letters in UNUNSUAL be arranged? For those arrangements, how many have all 3 U's together? Arranging Letters [11/08/1998] In how many ways can the letters in MISSISSIPPI be arranged? Suppose the 2 P's must be separated?... and other such problems. Arranging Marbles in Boxes [09/16/1998] Six marbles are placed in one of three different boxes. What is the probability that each box contains two marbles? Arranging Things on a Shelf [05/05/2006] Lucy has four vases--blue, yellow, red, and purple. How many ways can she arrange her vases in a row on a shelf? Balls in Boxes [05/05/1999] You have 2*t + 1 balls to put into 3 boxes, but the sum of the balls in 2 of the boxes should be more then the balls in the other box... Baseball Batting Orders [10/14/2001] How many possible batting orders are there for a team of nine players? Beads on a Bracelet [05/04/1997] How many different arrangements of 3 red and 3 blue beads on a bracelet are there? Bell Number [02/24/2002] I am trying to figure out how many different groups 50 people can be partitioned into. Bell Numbers [08/29/2001] I am looking for the formula for the number of different groups we can split a group of n different items into - order does not matter. Binomial Probability [04/14/1999] A multiple-choice exam probability question. Blocks of Seats [11/08/1998] In a row of 20 seats, in how many ways can 3 blocks of consecutive seats with 5 seats in each block be selected? And more such problems... Page:  1  2  3  4  5  6  7  8 [next>]

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