Question

Every day the teacher has her class of ten students line up for lunch. How many different ways can the students line up?3,628,8009010055

Answer 1

Answer:

3,628,800 ways

Explanation:

There are a total of 10 students.

• The first student can be any of the 10.

,

• The 2nd student can be any of the 9 remaining.

,

• The 3rd student can be any of the 8 remaining.

We can continue this way until we get to the last student.

Therefore, the number of ways for the students to line up is:

$\begin{gathered} 10!=10\times9\times8\times7\times6\times5\times4\times3\times2\times1 \\ =3,628,800 \end{gathered}$

There are 3,628,800 ways for the students to line up.