# Tag Archives: counting

## 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

## Divisible by 7

How many four digit positive integers divisible by have the property that, when the first and last digits are interchanged, the result is a (not necessarily four-digit) positive integer divisible by ? Source: NCTM Mathematics Teacher, October 2006 Solution Is … Continue reading

## Waiting in Line

In a movie theater line, people are behind Mark, who is places in front of Sam. If there are people in front of Sam, how many people are in line? Source: NCTM Mathematics Teacher, October 2006 Solution The figure illustrates … 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

## Pip Total as Prime Number

A pair of six-sided dice is tossed. What is the probability that the pip total is a prime number? Source: NCTM Mathematics Teacher, January 2006 Solution Number of possible outcomes Desirable outcomes Number of desirable outcomes Probability that the pip … Continue reading