Counting Principles (AQA GCSE Further Maths)

How many odd numbers greater than 30 000 can be formed from these digits

2           4            6           7           8

with no repetition of any digit?

Miriam’s date of birth is     14/09/2006

She makes a 4-digit number code using digits from her date of birth.

The 4-digit number she makes must

• not start with 0

• have all different digits.

How many codes can she make?

A 4-digit pin code for a lock is formed from the digits below, with no repeated digits allowed.

How many possible pin codes are multiples of 5?

In the Latin alphabet, there are 26 letters.

How many 3-letter passwords can be made from the Latin alphabet if no repeated letters are allowed and the password begins with either a V or a W?

How many 4-digit numbers can be made from the digits below, where repeated digits are allowed, and where the second digit is three times the third digit?

How many even 4-digit numbers greater than 7000 can be formed from the digits below, where no repeated digits are allowed?

The digits in the number 3,184,572 are used to form a 5-digit number with no repeated digits, where the first digit must be a prime number.

How many of these 5-digit numbers are even?

The letters from the word INTRICATE are used to make a 5-letter password with no repeated letters.

A rule for the 5-letter password is that no vowel must be next to another vowel, and that no consonant must be next to another consonant.

In the English language a vowel is considered as A, E, I, O, U.

How many possible passwords are there?