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)`=
`(n!)/(k!(n-k)!)`


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



330 ways