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andy62 | 01:49 Sun 23rd Sep 2007 | Quizzes & Puzzles

5 Answers

For some obscure reason I need to find out how many different arrangements of 4 letters I can choose from the the letters of SLEEPY SENATE.

Once again I find myself in disgreement with the book.

As I see it there are 5 cases.

4xE=1 way

3xE +1=28 ways

2xE+2xS=6 ways

All different=1680 ways

The last arrangement would be 2 alike letters plus 2 others.

I have broken this up into

2xS+1xE+1
2xS+2 from 6 (no E)
2xE+1XS+1
2xE+2 from 6 (no S)

which gives me 201 arrangements.

The book I'm using has a total of 504 arrangements for this part.

Who is right?

Scotsman Factfinders

fourpence off every thing

Answers

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mohill

Hi andy62! I agree with the book.
4E = 1
3E + 1 = 28
2E + 2S = 6
2E + 2different from each other = 6x7x6 = 252
2S + 2different from each other = 6x7x6 =252
4different from each other = 8x7x6x5 =1680
Total = 2219

You may have omitted the second to last possibility

Sonyme

There is a formula for this type of calculation which would be
12*11*10*9/(1*2*3*4) =495

Check any bookmakers diaries giving no of multiple bets fr any number of selections

This would equate to how many fourfold accumulators from 12 selections

andy62

Question Author

Thanks Mohill

I can see your logic (by the way I really do not like this topic) but I am struggling to see how you can treat the multiple S's or E's as single entities.

Most discombobulated!

Andy

mohill

4E there is obviously only 1 way they could be arranged

3E + 1 The 1 could be placed in any one of the 4 positions and in each case the 3Es take the three places remaining.
But the 1 could have been chosen from any of the 7 possible letters. Hence 4 x 7 = 28 arrangements.

2E + 2different from each other. 2Es can be placed in 6 different ways (see below). There are then 7 choices for th 1st 'different' and once it has been placed there are 6 choices for the 2nd 'different' one. So 6 x 7 x 6 =252

2E + 2S It is easier to see the permutations rather than use maths logic.
EESS ESES ESSE SESE SSEE SEES So 6 cases

2S + 1different
The logic is exactly the same as for 2E + 2different above.
Hence 6 x 7 x 6 = 252

All different from each other.
8 choices for the 1st position, then 7 , then 6 , then 5.
8 x 7 x 6 x 5 = 1680

1 + 28 + 252 + 6 + 252 + 1680 = 2219

I hope this helps.

andy62

Question Author

Thanks again mohill. Now it is clear.

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