Permutation -- Order matters
Combination -- Order doesn't matter
For the question, order does not matter. Hence, we have a combination.
The number of ways to select 3 students from 32 students is 32C3.
To evaluate "32C3", we need to know the combination formula:
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]Let's evaluate 32 C 3,
[tex]\begin{gathered} ^nC_r=\frac{n!}{(n-r)!r!} \\ ^{32}C_3=\frac{32!}{(32-3)!3!} \\ =\frac{32\cdot31\cdot30\cdot29!}{29!\cdot3!} \\ =\frac{32\cdot31\cdot30\cdot\cancel{29!}}{\cancel{29!}\cdot3!} \\ =\frac{32\cdot31\cdot30}{3\cdot2\cdot1} \\ =4960 \end{gathered}[/tex]Answer4960
