This can be done using the choose function.
The number of combinations are given by:
([n],[k])=(n!)/(k!(n-k)!)
where n is the total number of students and k is the number of students to be picked. So we have n=20 and k=5:
([20],[5])=(20!)/(5!(20-5)!)=(20!)/(5!15!)
Evaluate directly with a calculator:
(20!)/(5!15!)=15504
we can simplify this before calculation by hand:
(20!)/(5!15!)=(20times19times...times2times1)/(5times4times3times2times1times(15times...times1)
=((20times...times16)(15times...times1))/((5times...times1)(15times...times1))=((20times...times16)cancel(15times...times1))/((5times...times1)cancel(15times...times1))
=((color(red)20times19timescolor(blue)18times17timescolor(green)16))/((color(red)5timescolor(green)4times3timescolor(blue)2times1))
Simplify the numbers matched up by color:
=((4times19timescolor(green)9times17times4))/((1times1timescolor(green)3times1times1))
=((4times19times3times17times4))/((1times1times1times1times1))
=3times4times4times17times19
=48times323=15504
