Tag Archives: combinatorics

4-Digit Numbers Divisible by 7

Given the digits , and , find the probability that a four-digit number formed by using each of them only once is divisible by . Source: NCTM Mathematics Teacher, February 2008 Solution There are possible four-digit numbers using each only … Continue reading

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Distinct Triangles

How many distinct triangles can be constructed by choosing three vertices from among the corners of a unit cube? Source: NCTM Mathematics Teacher, February 2008 Solution We construct four triangles from three corners of a face for a total of … Continue reading

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Values From Three Coins

How many possible values can there be for three coins selected from among pennies, nickels, dimes, and quarters. Source: NCTM Mathematics Teacher, August 2006 Solution a) All three coins are the same Number of ways = b) Two of the … Continue reading

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Two Defective Tiles

An -by–ft area has been tiled with -foot-square tiles. Two of the tiles were defective. What is the probability that the two defective tile share an edge? Source: NCTM Mathematics Teacher, August 2006 Solution Area Vertical shared edges Horizontal shared … Continue reading

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Choosing an Integer

An experiment consists of choosing with replacement an integer at random among the numbers from to inclusive. If we let denote a number that is an integral multiple of and denote a number that is not an integral multiple of … Continue reading

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Making Triangles

You have six sticks of lengths , and cm. Find the number of noncongruent triangles that can be formed using three of these sticks as sides. Source: NCTM Mathematics Teacher, August 2006 Solution Three sticks make a triangle. There are … Continue reading

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U.S. Senate Committee

There are members in the U.S. Senate ( from each state). In how many ways can a committee of senators be formed if no state may be represented more than once? Source: NCTM Mathematics Teacher, August 2006 Solution We want … Continue reading

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Five Same Numbers

You roll five fair, six-sided dice, all at the same time. In that one roll, what is the probability of getting five of the same number? Source: NCTM Mathematics Teacher, September 2006 Solution When you roll five dice at the … Continue reading

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Second Number Larger Than The First

Suppose a six-sided die has sides numbered through . If a person throws the die two times, what is the probability that the second number will be larger than the first? Source: NCTM Mathematics Teacher, September 2006 Solution The desirable … Continue reading

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Bowling Pins

After rolling the first ball of a frame in a game of 10-pin bowling, how many different pin configurations can remain (assuming all configurations are physically possible)? Source: NCTM Mathematics Teacher, September 2006 Solution A pin configuration is made up … Continue reading

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