An orchestra conductor selects the first, second, and third chair violinists for an upcoming performance. If the conductor can choose from 210 combinations of first, second, and third chair violinists, how many violinists are in the orchestra.

Question

anonymous · Answer

A little confused with permutation and combinations.

anonymous · Answer

SAT question and not for marks just fyi.

anonymous · Answer

this question is kind of asking it backwards
what is $n$ so that 
$$_nP_3=120$$

anonymous · Answer

How do I solve it from there tho?

anonymous · Answer

try some numbers

anonymous · Answer

I know the answer is 7 just don't know the steps.

anonymous · Answer

$$10\times 9\times 8=720$$ way too big

anonymous · Answer

guess and check 
$$6\times 5\times 4=120$$ too small

anonymous · Answer

oh no it is not too small 
it is just right! so i would say the answer is 6, not 7

anonymous · Answer

oops 210 not 120
ok go bigger