SOLUTION: I don't know where to start with this one. It is in a chapter called intro to probability. nC8 = nC7 Find N the answer is: n=15 the 2 Ns and the numerals 7 and 8 are al

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: I don't know where to start with this one. It is in a chapter called intro to probability. nC8 = nC7 Find N the answer is: n=15 the 2 Ns and the numerals 7 and 8 are al      Log On

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Question 149900: I don't know where to start with this one.
It is in a chapter called intro to probability.
nC8 = nC7 Find N
the answer is: n=15
the 2 Ns and the numerals 7 and 8 are all subscripts.
Ineed to understand the steps involved. I know how to use basic algebra, it is the subscripts I don't know how to deal with.
thanks in advance for any help.
Heidi
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, the combination formula is:


So this means that and


So becomes:





Divide both sides by n%21. Notice how the n%21 terms cancel out.


Cross multiply


Expand 7%21 to get %287%29%286%29%285%29%284%29%283%29%282%29%281%29. Expand 8%21 to get %288%29%287%29%286%29%285%29%284%29%283%29%282%29%281%29


Notice how the terms %287%29%286%29%285%29%284%29%283%29%282%29%281%29 cancel out.


Simplify.


Rearrange the terms.



Divide both sides by 8%28n-8%29%21


Expand the factorials



Photobucket - Video and Image Hosting Cancel out the common terms.


%28n-7%29%2F8=1 Simplify


n-7=8 Multiply both sides by 8.


n=8%2B7 Add 7 to both sides.


n=15 Combine like terms on the right side.


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Answer:

So the answer is n=15