Tag Archives: Combinatorial

Playing Cards – Four of a Kind

Problem 5 cards are randomly drawn from a standard 52 card deck. What is the probability to get four of a kind. For example 4 different aces plus some additional card Solution The total number of ways to choose 5 …

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Computer Language Symbols

Problem A computer language is usingĀ 10 symbols and 26 letters. How many 6 digit words can be constructed using 3 different letters and 3 different symbols. How many different symbols can be constructed if the word has to start with …

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Probability of Selecting Two Balls of the Same Color

Problem You have 6 red balls, 7 green balls and 4 blue balls. You are asked to choose two balls. How many different ways you can select the balls if the color should match. How many different ways you can …

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Men and Women

Problem How many different couples we can make if we are asked to select 5 women from 10 candidates and 5 men from 12 candidates. Solution There are 10 choose 5 different ways to select the women: 10!/(10-5)!5! = 252 …

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Cars and Drivers

Problem We have 4 drivers and 4 cars. If two cars can only be driven by two drivers and the other two cars can be driven by any driver. How many different ways the drivers can drive the cars. Solution …

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Playing Cards – One Ace in each Hand

Problem In playing cards what is the probability that each of the four players gets an ace Solution Each player gets 13 cards out of 52 so there are: (52 choose 13)(39 choose 13)(26 choose 13)(13 choose 13) = (52!/39!13!)(39!/26!13!)(26!/13!13!) …

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Random Number in C

Problem We want to generate a random number between 100 and 499. what is the probability of generating a random number which has at least one digit = 1 for example 115. What is the probability of generating a random …

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