Exercise 1. Calculate

$$
\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1 - 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1}
$$

Only a numerical answer is expected here.
Solution to Exercise 1 By factoring the numerator by $4 \times 3 \times 2 \times 1$, the fraction becomes:

$$
\frac{4 \times 3 \times 2 \times 1 \times(6 \times 5-5)}{4 \times 3 \times 2 \times 1}=6 \times 5-5=25
$$

Remark: In general, a number of the form $1 \times 2 \times \ldots \times(n-1) \times n$ is often denoted $n$! and called the factorial of the integer $n$.

Comment from the graders: The exercise was very well solved overall! However, several students tried to reduce the fraction without first factoring the numerator by 4! ($4 \times 3 \times$ $2 \times 1$), and therefore did not find the solution.