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# just one little perms/combs Q Watch

1. Mymaths OW
I can answer everything else no problem except the last one.

A kid can't remember his dads number plate.
plate format: XX NN XXX

It has 2 Ds and 3 As in and the area code 07.

Therefore it's XX 07 XXX

How many possible number plates fit the bill?
2. (Original post by PKMN TRN JAM)
Mymaths OW
I can answer everything else no problem except the last one.

A kid can't remember his dads number plate.
plate format: XX NN XXX

It has 2 Ds and 3 As in and the area code 07.

Therefore it's XX 07 XXX

How many possible number plates fit the bill?
How many choices are there for where you can put the 2 Ds?

Then the As go into the remaining gaps.
3. (Original post by notnek)
How many choices are there for where you can put the 2 Ds?

Then the As go into the remaining gaps.
the 2 Ds can go anywhere,

So 2!? or 5C2? then what?
4. (Original post by PKMN TRN JAM)
the 2 Ds can go anywhere,

So 2!? or 5C2? then what?
2! is 2 and there are clearly more than 2 choices for the 2Ds.

5C2 is correct.

Now look at some examples:

DX07DXX
DD07XXX
XX07DXD

For each of these (of which there are 5C2), there is only one way of slotting in the 3 As.

So number of possible number plates = number of ways of slotting in the 2 Ds = 5C2

An alternative method is to consider how many choices there are for placing the 3 As. Since 5C2=5C3, this method will give you the same answer.

Does this all make sense?
5. (Original post by notnek)
2! is 2 and there are clearly more than 2 choices for the 2Ds.

5C2 is correct.

Now look at some examples:

DX07DXX
DD07XXX
XX07DXD

For each of these (of which there are 5C2), there is only one way of slotting in the 3 As.

So number of possible number plates = number of ways of slotting in the 2 Ds = 5C2

An alternative method is to consider how many choices there are for placing the 3 As. Since 5C2=5C3, this method will give you the same answer.

Does this all make sense?
Yeah I understand, thanks a bunch.

(I would rep you but I reached my limit )

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