4!=4*3*2*1=24
11!=11*10*9*8*7*6*5*4*3*2*1=39916800
7!=7*6*5*4*3*2*1=5040
n choose k
how many ways are there to choose k rollercoasters from n choices?
[tex] \left(\begin{array}{ccc}n\\k\end{array}\right) [/tex]=[tex] \frac{n!}{k!(n-k)!} [/tex]
[tex] \left(\begin{array}{ccc}11\\4\end{array}\right) [/tex]=[tex] \frac{11!}{4!(11-4)!} [/tex]=[tex] \frac{39916800}{24(7)!} [/tex]=[tex] \frac{39916800}{24(5040)} [/tex]=[tex] \frac{39916800}{120960} [/tex]=330
330 ways
