Solving Permutations and Combinations. Please explain to me how to solve n + 1 Cn − 1 = 15? If possible please add more tips. Thanks.

1 Answer
Alan P. · Shwetank Mauria
Jan 18, 2018

n=5

Explanation:

""_(n+1)C^(n-1)
color(white)("XXX")=((n+1)!)/((n-1)!2!)

color(white)("XXX")=((n+1) * (n))/2color(white)("xxx")=15

color(white)("XXX")rArr(n+1) * n =30

assuming n > 0
we can solve this by observation (what 2 successive positive numbers have a product of 30?)
or
continuing with the above
color(white)("XXX")rArrn^2+n-30=0

color(white)("XXX")rArr(n-5)(n+6)=30
whose only positive solution is n=5

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