# Perms And Coms

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#1
Find the number of permutations of the letters of the word TOPOLOGY. In how many of these permutations are no two Os together?
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#2
How many different signals can be made from one green, three identical red and two identical blue flags if at least five of them are used?
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5 years ago
#3
We are not here to do your work for you. I have given you a hint for one question so please take time to think over it.
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5 years ago
#4
If I asked how many ways can you organise the letters abc you would say 3! So this is like that except now some letters are repeated so we are going to end up with some identical words if we do it this way. So we need to do some division to get rid of the identical ones.

Complete this:
1 T
3 O
? P
? L
? G
? Y

So if we did it like the abc example, how many words would we have?
But, for example, we have 3Os so there are 3! ways we can organise the Os, so we need to divide by something...
Do the same for the other letters with repetition.

For no two Os together, treat OO as one letter. So now you have:
1 T
2 O
Etc
So work out how many words there can be like this.
But this is working out how many have OO together, so you need to subtract this number from something to get the answer.

I hope this helps somehow. It's hard to explain it without just giving the calculations. :-/

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