Question

Consider all five-digit numbers that can be created from the digits 0-9 0 - 9 where the first and last digits must be odd and no digit can repeat. What is the probability of choosing a random number that starts with 7 7 from this group? Enter a fraction or round your answer to 4 4 decimal places, if necessary.

Answer 1

There are a total of 5 digits that can be chosen for the first digit (1, 3, 5, 7, and 9), and 5 digits that can be chosen for the last digit (1, 3, 5, 7, and 9). Since no digits can repeat, the number of choices for the middle 3 digits is 9 * 8 * 7 = 504. Therefore, there are a total of 5 * 504 * 5 = 10,080 five-digit numbers that can be formed from the digits 0-9 where the first and last digits are odd and no digit can repeat.

Of these numbers, there are 504 numbers that start with 7, because there are 504 choices for the middle 3 digits and 1 choice for the first digit. Therefore, the probability of choosing a random number that starts with 7 from this group is 504 / 10,080 = 0.05, or approximately 5%.