# Combination Word Problems

### Solutions

1How many different combinations of management can there be to fill the positions of president, vice-president and treasurer of a football club knowing that there are 12 eligible candidates?

2How many different ways can the letters in the word "micro" be arranged if it always has to start with a vowel?

3How many combinations can the seven colors of the rainbow be arranged into groups of three colors each?

4How many different five-digit numbers can be formed with only odd numbered digits? How many of these numbers are greater than 70,000?

5How many games will take place in a league consisting of four teams? (Each team plays each other twice, once at each teams respective "home" location)

610 people echange greetings at a business meeting. How many greetings are exchanged if everyone greets each other once?

7How many five-digit numbers can be formed with the digits 1, 2 and 3? How many of those numbers are even?

8How many lottery tickets must be purchased to complete all possible combinations of six numbers, each with a possibility of being from 1 to 49?

9How many ways can 11 players be positioned on a soccer team considering that the goalie cannot hold another position other than in goal?

## 1

How many different combinations of management can there be to fill the positions of president, vice-president and treasurer of a football club knowing that there are 12 eligible candidates?

The order of the elements does matter.

The elements cannot be repeated.

## 2

How many different ways can the letters in the word "micro" be arranged if it always has to start with a vowel?

The words will begin with **i** or **o** followed by the remaining 4 letters taken from 4 by 4.

The order of the elements does matter.

The elements cannot be repeated.

## 3

How many combinations can the seven colors of the rainbow be arranged into groups of three colors each?

The order of the elements does not matter.

The elements cannot be repeated.

## 4

How many different five-digit numbers can be formed with only odd numbered digits? How many of these numbers are greater than 70,000?

The order of the elements does matter.

The elements cannot be repeated.

n = 5 k = 5

The odd numbers greater than 70,000 have to begin with 7 or 9. Therefore:

## 5

How many games will take place in a league consisting of four teams? (Each team plays each other twice, once at each teams respective "home" location)

The order of the elements does matter.

The elements cannot be repeated.

## 6

10 people echange greetings at a business meeting. How many greetings are exchanged if everyone greets each other once?

The order of the elements does not matter.

The elements cannot be repeated.

## 7

How many five-digit numbers can be formed with the digits 1, 2 and 3? How many of those numbers are even?

The order of the elements does matter.

The elements are repreated.

If the number is even it can only end in 2.

## 8

How many lottery tickets must be purchased to complete all possible combinations of six numbers, each with a possibility of being from 1 to 49?

The order of the elements does not matter.

The elements cannot be repeated.

## 9

How many ways can 11 players be positioned on a soccer team considering that the goalie cannot hold another position other than in goal?

Therefore, there are 10 players who can occupy 10 different positions.

The order of the elements does matter.

The elements cannot be repeated.