Combinations of unknown number $n$

Question

All members of a group play basketball, while all except one play ice hockey. The number of possible basketball teams of $5$ members each is the same as the number of possible ice hockey teams of $6$ members each. How many members are there in the group?

I am unable to derive a formula for the number of teams.

Answer - $15$

score 3 · Accepted Answer · answered Aug 15 '15 at 17:26

3

The key is to identify your equality. We have \begin{align*} {n\choose5} &= {n-1\choose6} \\ \rightarrow \frac{n!}{5!(n-5)!} &= \frac{(n-1)!}{6!(n-7)!} \end{align*}

And you can solve for your result $n$ from there with a bit of manipulation.

answered Aug 15 '15 at 17:26

miradulo

3,782

score 0 · Answer 2 · answered Aug 15 '15 at 17:30

0

$n\choose5$=$n-1\choose6$

Solve this equation and you will get it.

answered Aug 15 '15 at 17:30

Soham

9,990

Combinations of unknown number $n$

2 Answers2