Question

There are 12 students in a class, and 5 of them will be chosen to go on a field trip. How many ways can these students be chosen?

Answer 1

Answer:

792 ways

Explanation:

The number of students in the class = 12

If 5 of them are to go on the field trip, since the order doesn’t matter. the number of ways that these children could be chosen can be calculated using combination.

$^{12}C_5$

Recall:

$^nC_r=\frac{n!}{(n-r)!r!}$

Therefore:

$\begin{gathered} ^{12}C_5=\frac{12!}{(12-5)!5!} \\ =\frac{12\times11\times10\times9\times8\times7!}{7!\times5!} \\ =\frac{12\times11\times10\times9\times8}{5!} \\ =\frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1} \\ =\frac{95040}{120} \\ =792 \end{gathered}$

The students can be chosen in 792 ways.