HORSE TRAINING
A horse trainer boards an owner's horse for a minimum of 6 months during training. As a horse comes into their program.
the trainer randomly assigns a number to them. Each number consists of 6 digits ranging from 1 to 9. If the digits cannot repeat, find the probability that a randomly generated number is 325876. Express your answer as a fraction in simplest form.

To find the probability that a randomly generated number is 325876, we need to determine the total number of possible 6-digit numbers without repeating digits and compare it to the number of favorable outcomes (which is 1 in this case).

The total number of possible 6-digit numbers without repeating digits can be calculated as follows:

For the first digit, we have 9 options (1 to 9).

For the second digit, we have 9 options (any digit except the one already chosen).

For the third digit, we have 8 options (any digit except the two already chosen).

Similarly, for the fourth, fifth, and sixth digits, we have 7, 6, and 5 options, respectively.

Therefore, the total number of possible 6-digit numbers without repeating digits is:

9 × 9 × 8 × 7 × 6 × 5 = 136,080.

Since there is only 1 favorable outcome (the number 325876), the probability of randomly generating the number 325876 is:

1 / 136,080.

Hence, the probability is 1/136,080, which is already expressed as a fraction in simplest form.

greentoowon greentoowon · Answer 2 · 2024-04-18T18:41:40+02:00

1. Consider the total number of possible outcomes.

2. There are 9 choices for the first digit.

3. There are 8 choices for the second digit (excluding the first one).

4. There are 7 choices for the third digit (excluding the first two).

5. There are 6 choices for the fourth digit (excluding the first three).

6. There are 5 choices for the fifth digit (excluding the first four).

7. There are 4 choices for the sixth digit (excluding the first five).

8. So, the total number of possible outcomes is 9 * 8 * 7 * 6 * 5 * 4.

9. Now, consider the desired outcome, which is the number 325876.

10. There's only one outcome that matches the desired number.

11. Therefore, the probability of randomly generating the number 325876 is 1 divided by the total number of possible outcomes.

12. Simplify the fraction.

13. So, the probability is 1/60480.