# Tag Archives: counting

## 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

## 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

## Two Even Digits

The number is a four-digit number having two zeros and two even digits that are not zeros. How many four-digit numbers besides can also be described this way? Source: NCTM Mathematics Teacher, February 2008 Solution First, choose a way to … Continue reading

## Divisible by 11 or 13 or Both

What is the sum of the integers between and that are divisible by or (or both)? Source: NCTM Mathematics Teacher, February 2008 Solution integers divisible by are and integers divisible by are . The multiples of form an arithmetic progression … Continue reading

## 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