Answer:
There are 1860480 speech arrangements
Step-by-step 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