Category Archives: Math and Probability - Page 2

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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Probability Selecting Marbles

Problem A bag of marbles containing 4 white marbles and 6 red marbles. If we randomly select two marbles from the bag what is the probability that the selected marbles are of different colors in other words one white and …

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Playing Cards

Problem In playing cards what is the probability to get exactly one pair (for example (1,1), (2,2)) if we draw 5 cards Solution Step one is to compute how many possibilities we have if we draw 5 cards without any …

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Binomial Theorem Example

Subsets Using Binomial Theorem How many subsets we can make from the numbers between 1 and 5 Solution The naive way to compute that is to enumerate all possibilities as follows: Groups of 1: 1, 2, 3, 4, 5 Groups …

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Making Binary Numbers

Problem Given four binary digits all ones 1111 and two binary digits all zeros 00 we need to create a six digit binary number using these ones and zeros such that no two zeros are next to each other. How …

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