Assume that 3 digits are selected at random from the set { 2, 5, 6, 8, 9 } and are arranged in random order.
What is the probability that the resulting 3-digit number is less than 900?
4 out of 5 that the number will be less than 900
To calculate the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Possible Outcomes:
Since we are selecting 3 digits from the set {2, 5, 6, 8, 9} and arranging them in random order, there are a total of 5 choices for the first digit, 4 choices for the second digit, and 3 choices for the third digit. Therefore, the total number of possible outcomes is 5 * 4 * 3 = 60.
Number of Favorable Outcomes:
To find the number of favorable outcomes, we need to consider the conditions for the resulting 3-digit number to be less than 900.
1. If the first digit is 2:
The second digit can be any of the remaining 4 digits (5, 6, 8, 9), and the third digit can be any of the remaining 3 digits. So there are 4 * 3 = 12 possible outcomes.
2. If the first digit is 5:
The second digit can be any of the remaining 3 digits (6, 8, 9), and the third digit can be any of the remaining 2 digits. So there are 3 * 2 = 6 possible outcomes.
3. If the first digit is 6:
The second digit can be any of the remaining 2 digits (8, 9), and the third digit can be any of the remaining 1 digit. So there are 2 * 1 = 2 possible outcomes.
Therefore, the total number of favorable outcomes is 12 + 6 + 2 = 20.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 20 / 60
= 1/3
≈ 0.3333
So, the probability that the resulting 3-digit number is less than 900 is approximately 0.3333 or 1/3.