Question

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

Answer 1

`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`