Step 1:
To select or choose 5 students out of 21 students involve combination.
In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter.
Step 2:
Use the formula below to find the number of ways 5 students can be selected from 21 students.
n = 21 and r = 5
[tex]^nC_r\text{ = }\frac{n!}{(n\text{ - r)! r !}}[/tex]Step 3:
[tex]\begin{gathered} ^{21}C_5\text{ = }\frac{21!}{(21\text{ - 5)! 5!}}\text{ ways} \\ =\text{ }\frac{21!}{16!\text{ }\times\text{ 5!}} \\ =\text{ }\frac{21\text{ }\times\text{ 20 }\times\text{ 19 }\times\text{ 18 }\times\text{ 17 }\times\text{ 16!}}{16!\text{ }\times\text{ 5 }\times\text{ 4 }\times\text{ 3 }\times\text{ 2 }\times\text{ 1}} \\ =\text{ }\frac{21\text{ }\times\text{ 20 }\times\text{ 19 }\times\text{ 18 }\times\text{ 17}}{5\text{ }\times\text{ 4 }\times\text{ 3 }\times\text{ 2 }\times\text{ 1}} \\ =\text{ }\frac{2441880}{120} \\ =\text{ 20349 ways} \end{gathered}[/tex]Final answer
