Question

An amusement park has 11 roller coasters. In how many ways can you choose 4 of the roller coasters to ride during your visit to the park?

Answer 1

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?

$\left(\begin{array}{ccc}n\\k\end{array}\right)$=$\frac{n!}{k!(n-k)!}$

$\left(\begin{array}{ccc}11\\4\end{array}\right)$=$\frac{11!}{4!(11-4)!}$=$\frac{39916800}{24(7)!}$=$\frac{39916800}{24(5040)}$=$\frac{39916800}{120960}$=330



330 ways