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=(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=(9!)/(4!(9-4)!) \\ C=(362880)/(4!\cdot5!)=(362880)/(2880) \\ C=126 \end{gathered}`

There are 126 possible combinations.