SOLUTION: If 9 combination n : 8combination (n-2) = 9:4, find the values of n.

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Question 1207518: If 9 combination n : 8combination (n-2) = 9:4, find the values of n.
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!




"cross multiply"



Rewrite using definition of C(n,r), and simplify





Rearrange factors so that each fraction has "similar" factorials



Simplify and solve













n = -8 or n = 5

Ignore the negative solution which makes no sense.

ANSWER: n=5

CHECK:
C(9,n)=C(9,5)=126
C(8,n-2)=C(8,3)=56
126/56=9/4

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Or, for a faster solution which gives you no practice with manipulating factorials....

n=3? C(9,3)=84; C(8,1)=8; 84/8 not = 9/4 No
n=4? C(9,4)=126; C(8,2)=28; 126/28 not = 9/4 No
n=5? C(9,5)=126; C(8,3)=56; 126/56 = 9/4 YES
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

The tutor greenestamps has a great solution. It's probably the method your teacher wants you to follow.

If your teacher allows you to use a spreadsheet then you can use the Combin function to find the answer very quickly.
Avoid the Choose function since that's something entirely different.

nA = Combin(9, n)B = Combin(8, n-2)A/BIs A/B = 9/4 = 2.25?
236136No
384810.5No
4126284.5No
5126562.25Yes
684701.2No
736560.642857 (approx)No
89280.321429 (approx)No
9180.125No
According to the table, n = 5 will turn "9 combination n" into 126 and "8 combination (n-2)" becomes 56.
126/56 = 9/4 = 2.25
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