# Tag Archives: combinatorics

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## Largest of Five Integers

A set contains five integers. When distinct elements of this set are added together, two at a time, the complete list of different possible sums is , and . What is the largest of the five integers in the set? … Continue reading

## Same Difference

If fifteen distinct whole numbers are randomly selected from to inclusive, determine the probability that two pairs of these numbers will have the same difference. Source:NCTM Mathematic Teacher, January 2006 Solution What are the possible difference values? There are possible … Continue reading