Question

In how many ways can a teacher arrange 10 students in the front row if there are 60 total students?

Answer 1

@Michele_Laino

Answer 2

I think that the requested way is given by the number of all possible subsets of 10 students that we can make using 60 students

Answer 3

do you know what is that number?

Answer 4

its permutations

Answer 5

no, since we have to make subsets of 10 students, using 60 students in total

Answer 6

oh

Answer 7

do you know the binomial coefficients?

Answer 8

no

Answer 9

the number which I mentioned above is the subsequent binomial coefficient:
\[\left( {\begin{array}{*{20}{c}}
{60} \\
{10}
\end{array}} \right) = \frac{{60!}}{{10!\left( {60 - 10} \right)!}}\]

Answer 10

so the answer is 6.974076e+139 @Michele_Laino

Answer 11

I got this:
75394027566
since we have:
\[\left( {\begin{array}{*{20}{c}}
{60} \\
{10}
\end{array}} \right) = \frac{{60!}}{{10!\left( {60 - 10} \right)!}} = \frac{{60!}}{{10!\;50!}} = {\text{75394027566}}\]