Product rule for counting

An ice cream van sells 7 flavours of ice cream and 4 different toppings.

Nadia chooses one flavour and one topping.

Work out the number of different combinations Nadia can choose.

Ola is choosing an outfit.

She has 3 shirts: red (R), blue (B) and green (G).

She has 2 pairs of shorts: black (K) and white (W).

List all the possible outfits Ola can choose. One outfit, RK, has been done for you.

A bistro menu has 5 starters, 8 main courses and 4 desserts.

Callum chooses one starter, one main course and one dessert.

Work out the number of different three-course meals Callum can choose.

A cafe sells 3 hot drinks: tea (T), coffee (C) and hot chocolate (H).

It sells 2 cakes: flapjack (F) and brownie (B).

Noah chooses one hot drink and one cake.

List all the possible combinations Noah can choose.

Imani has 5 tops, 4 pairs of trousers and 3 pairs of shoes.

She chooses one top, one pair of trousers and one pair of shoes.

Work out the number of different outfits she can choose.

There are 9 boys and 12 girls in a drama club.

One boy and one girl are to be chosen to present the end of term show.

Work out the number of different ways the pair can be chosen.

Bag A contains three cards numbered 1, 2 and 3.

Bag B contains two cards numbered 5 and 7.

Erin takes one card from bag A and one card from bag B.

Write down all the possible pairs of cards Erin can take.

A pizzeria offers x different pizzas and 6 different side orders.

There are 54 different ways to choose one pizza and one side order.

Work out the value of x.

Ali throws a fair coin 3 times.

Each throw lands on heads (H) or tails (T).

List all the possible outcomes of the 3 throws. One outcome, HHH, has been done for you.

A 3-digit code is made using the digits 1, 2, 3, 4 and 5.

A digit cannot be used more than once in a code.

Work out the number of different codes.

A locker code is made up of one letter followed by two digits.

The letter is chosen from the 26 letters A to Z.

Each digit is chosen from 0 to 9, and digits may repeat.

Work out the number of different codes that are possible.

A locker code is a letter followed by a prime number.

The letter is chosen from P, Q and R.

The prime number is chosen from 3 and 7.

List all the possible locker codes.

A cafe sells 6 different sandwiches and 3 different desserts, and also sells n different drinks.

A meal deal is one sandwich, one drink and one dessert.

There are 108 different meal deals.

Work out the value of n.

There are 14 netball teams in a league.

Each team plays every other team twice, once at home and once away.

Work out the total number of games played in the league.

Here are three digit cards.

2   5   8

Ravi uses two different cards each time to make two-digit numbers.

List all the two-digit numbers Ravi can make.

8 runners take part in a race.

Gold, silver and bronze medals are awarded to the first, second and third runners.

Work out the number of different ways the three medals can be awarded.

There are 12 teams in a hockey league.

Every team plays every other team twice, once at home and once away.

Work out the total number of matches in the league.

There are 20 students in a chess club.

Two of the students are to be chosen to enter a doubles tournament as a pair.

Work out the number of different pairs that can be chosen.

A password has 1 letter from A to F, then 2 digits from 0 to 9, then 1 symbol from &, £ or %.

1. Work out the number of different passwords if digits may be repeated.
2. Work out the number of different passwords if the two digits must be different.

A sandwich shop offers a meal deal.

Customers choose one of 8 sandwiches, one of 5 packets of crisps and one of 3 drinks.

Kai says, "There are more than 100 different meal deals."

Show that Kai is correct.

Spinner A has three equal sections numbered 1, 2 and 3.

Spinner B has two equal sections numbered 4 and 5.

Both spinners are spun and the two numbers are multiplied together.

List all the possible products.

A 3-digit number is made using the digits 0 to 9.

The first digit cannot be 0, and no digit can be used more than once.

Work out the number of different 3-digit numbers that can be made.

The passcode for a tablet is a 4 digit number.

The first digit cannot be 0.

Digits may repeat.

1. Work out the number of different passcodes that are possible.
2. Ruby does not know the passcode. She types one 4 digit number at random, with a non-zero first digit. Write down the probability that Ruby types the correct passcode.

The code for a padlock is made up of 3 digits.

Each digit is chosen from 1 to 9.

All three digits must be different.

The code must be an odd number.

Work out the number of different codes that are possible.