Adam chooses the colours for a new team shirt. The shirt has two colours. There are four colours to choose from: yellow, blue, white, and red. Write the two missing combinations. The shirt could be a) yellow and blue, b) yellow and white, c) yellow and red, d) blue and white, e) what and what, or f) what and what.
So we know that Adam’s been given the job to choose the colours for his new team shirts. And we know from the second sentence and by looking at the illustration that this is going to be a stripy shirt; it’s going to have two colours. Adam’s got a choice about which colours he uses. There are four colours that he can choose from. And we’re told that these are yellow, blue, white, and red. So Adam can choose two of these colours and put them in different combinations.
And there are actually six different combinations that are possible. We’re given four of them: a, b, c, and d. And then, we’re asked to write the two missing combinations e and f. When we’re asked to find all the possible combinations of a set of colours or a set of numbers, it’s always good to keep one thing the same and to change everything else. We find all the possible combinations with that one thing.
So if Adam chose yellow as one of his colours, we can work out all the possible combinations by keeping yellow the same and just changing the second colour: yellow and blue, yellow and white, yellow and red. There’s no other combination we can make involving the colour yellow. But none of these three combinations are our missing combinations because they’re already on the list: yellow and blue, yellow and white, yellow and red.
Now, let’s look at all the combinations we can make with blue as one of the colours. We don’t need to write down blue and yellow because we’ve already covered that one. So we’re just left with blue and white and blue and red. Let’s go back to our list and see whether we can fill in any of the missing combinations.
Blue and white is d on the list so that’s already been written down for us. But the blue and red shirt is a combination that isn’t written down yet. So we know one of the missing combinations is blue and red. We’re running out of possibilities now. Let’s find out the different combinations that we can make using white as one of the colours. So we’ll keep white the same and change the second colour.
White and yellow: we don’t need to write that one down because we covered that when we thought about all the combinations with yellow in them. White and blue: we’ve already covered that one. And white and red; this is our final missing combination. There’s no need to go through all the answers where we keep red the same and change the second colour because we’ve already found all three possibilities when we looked at the other colours.
The two missing combinations are blue and red and white and red. And of course, we can give these answers in the opposite order. It will still be correct. We found all the different possibilities by keeping one colour the same and changing the second colour to find the different combinations.
So there are six different combinations of colours that Adam could choose for his new team shirt and the two that are missing are blue and red and white and red.