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# NEED HELP ASAP WITH BIO/MATH QUESTION!!

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If I have 56 nuclotide bases and each DNA model can contain 4 different bases, how many different combinations of DNA models can I have?

Oct 23, 2017

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Mmm

Are you asking how many ways can 4 elements be chosen from 56?

(for this answer I have assumed order doesn count and each element can only be chosen once)

If so then the answer is

56C4

nCr(56,4) = 367290

Oct 23, 2017
edited by Melody  Oct 24, 2017
#2
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nCr[56 + 4  - 1], 4 =59C4 =455,126

Oct 23, 2017
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Why guest? More explanation is needed...

Melody  Oct 23, 2017
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My understanding is that the 4 bases can be repeated, such as:AAAA, CCCC, GGGG and TTTT. The formula I used is the Binomial expansion with repeats allowed.

Oct 23, 2017
#5
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ok thanks for the input,

Maybe but it does say '4 different bases' though ://

If they can be repeated then I think it would be  56^4 choices = 56^4 = 9834496 possibilities.

Melody  Oct 23, 2017
edited by Melody  Oct 23, 2017
#6
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You could be right. I have a Math Dictionary and gives the following:
1-Combinations with repetitions: Each element can be chosen more than once for a particular combination. The number of possible combinations is then [n + r -1], r.
Example n=4, r=2  a, b, c, d: aa, ab, ac, ad,
bb, bc, bd,
cc, cd,
dd,
[4 + 2 -1], 2 =5C2 = 10

Oct 23, 2017
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Ah yes, I was taking AB to be different from BA. I am not sure if order counts in the initial question or not. ....

Melody  Oct 24, 2017