Question

# Consider all four-digit numbers that can be created from the digits 0-9 where the first and last digits must be even and no digit can repeat.

Probability and combinatorics
Consider all four-digit numbers that can be created from the digits 0-9 where the first and last digits must be even and no digit can repeat. Assume that numbers can start with 0. What is the probability of choosing a random number that starts with 8 from this group? Enter a fraction or round your answer to 4 decimal places, if necessary.

2021-09-05

The first and last digits should be even. Hence, Total number of numbers possible

$$\displaystyle={5}\cdot{4}\cdot{8}\cdot{7}={1120}$$

Total number that starts with

$$\displaystyle{2}={4}\cdot{8}\cdot{7}={224}$$

Hence, P(Stars with 2)

$$\displaystyle=\frac{224}{{1120}}=\frac{1}{{5}}$$