If 5 students in a class of 20 will be chosen to present a speech, how many
speech arrangements are there?

There are 1860480 speech arrangements

Explanation:

There are 5 spots for 5 students to present a speech. So 5 of the 20 students will need to fill the spaces. Think of it like a table with 5 positions to be filled. ▢▢▢▢▢

Assuming no student can present more than once, we start off with 20 possible students to present first, 19 to present second, and so on until 5 students have presented. Following this method:

20 x 19 x 18 x 17 x 16

This is known as a Permutation (the nPr function on your calculator)

The formula for permutations are n!/(n-r)!

n being the number available and r is the number of positions.

Plugging our values in, we get:

20!/(20-5)!

= 20!/15!

= 20 x 19 x 18 x 17 x 16 x 15!/ 15!  ~ 15! can be crossed leaving

= 20 x 19 x 18 x 17 x 16 = 1860480