There are 137 NRICH Mathematical resources connected to Combinations, you may find related items under Decision mathematics and combinatorics.
Broad Topics > Decision mathematics and combinatorics > Combinations
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
My coat has three buttons. How many ways can you find to do up all the buttons?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
An environment which simulates working with Cuisenaire rods.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
Can you fill in the empty boxes in the grid with the right shape and colour?
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
How many six digit numbers are there which DO NOT contain a 5?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Which of these games would you play to give yourself the best possible chance of winning a prize?
Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
Find all the numbers that can be made by adding the dots on two dice.
Ben has five coins in his pocket. How much money might he have?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Investigate the different ways you could split up these rooms so that you have double the number.
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
If you had 36 cubes, what different cuboids could you make?
This activity investigates how you might make squares and pentominoes from Polydron.