If you have a five bit string ABCDE, how many strings can you make that have A before C and C before E?

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- Apr 7th 2008, 12:00 PMFrostkingpermutation question
If you have a five bit string ABCDE, how many strings can you make that have A before C and C before E?

- Apr 7th 2008, 12:07 PMPlato
- Apr 7th 2008, 12:16 PMFrostkingreply to permutation question
So, you are saying since there are 120 total ways to arrange a five bit string with ABCDE, there would be 20 of these in which A is before C and C is before E? Can I then think of it as choosing the other two members D and B in 5 x 4 ways? Or is that in error? Thanks so much for your prompt help!

- Apr 11th 2008, 01:16 AMlekge
since there got 5 string, let this to be 5 empty space

_ _ _ _ _

given situation some thing look like A->C->E (A before C before E)

from this 5 empty space, choose 3 of this 5, therefore there have C(5,3)=10

ways to put A C E, this left B and D, after finish put A C E, there left 2 free space for B and D. Hence C(5,3)*2*1=20 - Apr 11th 2008, 05:35 AMSoroban
Hello, Frostking!

Quote:

If you have a five bit string ABCDE, how many strings can you make

that have A before C and C before E?

Since A, C, E__will__appear in alphabetical order,

. . the only issue is the placement of B and D.

And there are:. $\displaystyle P(5,2) \:=\:20$ ways.

- Apr 11th 2008, 07:48 AMFrostkingPermutation question help
Thank you Soroban and Lekge for adding your explanations. I really appreciate the help!!!!!