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**Year 3 to Year 6: Button Up Some More**

TI have a jacket which has four buttons.

Sometimes, I do the buttons up starting with the top button. Sometimes, I start somewhere else.

How many different ways of buttoning it up can you find?

Look back at the number of different ways you found for buttoning up three buttons and four buttons.

Can you predict the number of ways of buttoning up a coat with five buttons?

Six buttons ...?

Then switch the last two numbers,1243 .

As you can't swap them again, swap the second number in the solution to another but not the first number. In this case it's one eg: 1324 .

Now swap the last two numbers' places - 1342 .

As before you swap the second number in the solution with the only number which hasn't been second: 1432 .

And again swap the last two numbers' places - 1423 .

To get all solutions just use the same method but change the first number until all numbers have been in first place and you should end up with the 24 different combinations as follows;

1234 , 1243 , 1324 , 1342 , 1432 , 1423 , 2341 , 2314 , 2413 , 2431 , 2134 , 2143 , 3214 , 3241 , 3412 , 3421 , 3124 , 3142 , 4321 , 4312 , 4231 , 4213 , 4123 , 4132 .

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