# Tag Archives: combination

## 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

## 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

## 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

## Numbers Greater Than 5,000,000

Using all the digits and , how many distinct integers greater than can be formed? Source: NCTM Mathematics Teacher, January 2006 Solution The first digit must be a or a . Case 1: _ _ _ _ _ _ Since … Continue reading

## Vigornii Alphabet

In the Vigornii alphabet there are consonants and vowels. How many different arrangements of letters can be made if exactly vowels must be used and no repetition of letters is allowed? Source: NCTM Mathematics Teacher, February 2006 SOLUTION 1. Choose … Continue reading

## Carnival Chance

You are at a carnival and decide to play a game that can win you a beautiful stuffed teddy bear. For one dollar, you get to randomly pick two numbered balls out of a jar without replacement and without looking. … Continue reading

## Necklaces

In how many ways can a necklace be made using 5 identical red beads and 2 identical blue beads? Source: http://www.mathcircles.org SOLUTION Imagine the 7 positions of the beads are represented by the 7 letters . Of these 7 positions … Continue reading

## TENNESSEE

A 4-letter word can be made from the letters of the word . For example, , and so on. Each word is an ordering ofÂ four letters. Find the number of such distinguishable orderings. Source: submitted by Jimel Mariano 9/25/2011 SOLUTION … Continue reading