Question

1. A lock has four dials. On each dial are the digits 0 to 9. Numbers cannot be repeated. How many possible combinations are there?

Answer 1

Combinations without repetitions are represented by the following expression:

$\begin{gathered} C=\frac{n!}{r!(n-r)!} \\ \text{By the information given:} \\ n=9\text{ and r=4} \end{gathered}$

Then, we can substitute in the equation:

$\begin{gathered} C=\frac{9!}{4!(9-4)!} \\ C=\frac{362880}{4!\cdot5!}=\frac{362880}{2880} \\ C=126 \end{gathered}$

There are 126 possible combinations.