Counting Principles Practice Questions

How many different meal deals are possible?

At the end of term, gold, silver and bronze awards are given to three different students from a group of $8$ students. No student can receive more than one award.

In how many different ways can the three awards be given out?

The five letters

P R I M E

are arranged in a line. Each letter is used exactly once.

The arrangement must begin with a vowel and end with a consonant.

How many different arrangements are possible?

You must show your working.

A membership code is made up of two letters followed by three digits, for example BQ 407.

• The letters are chosen from the $26$ letters of the alphabet and must be different from each other.
• Each digit may be any of $0$ to $9$ and digits may be repeated.
• The final digit must be odd.

How many different membership codes are possible?

You must show your working.

How many different five-digit integers can be made?

How many of these five-digit integers are even?

You must show your working.

Four-digit integers are made using the digits

0 1 4 5 7 9

No digit is used more than once in an integer.

The integers are multiples of $5$ and are greater than $5000$.

How many different integers can be made?

You must show your working.

A four-character code is made up of characters chosen from

• the six letters A B C D E F
• the ten digits 0 1 2 3 4 5 6 7 8 9

Each of the four positions may be a letter or a digit, and characters may be repeated.

How many of these codes contain at least three digits?

You must show your working.