Final answer:
To calculate the probability that a randomly selected five-digit natural number has the form abcde where 1 ≤ a ≤ b ≤ c ≤ d ≤ e ≤ 9, you need to determine the total number of possible numbers that meet this condition and divide it by the total number of possible five-digit natural numbers.
Step-by-step explanation:
To calculate the probability that a randomly selected five-digit natural number has the form abcde where 1 ≤ a ≤ b ≤ c ≤ d ≤ e ≤ 9, we need to determine the total number of possible numbers that meet this condition and divide it by the total number of possible five-digit natural numbers.
Since 1 ≤ a ≤ b ≤ c ≤ d ≤ e ≤ 9, there are 9 choices for each digit: 1, 2, 3, 4, 5, 6, 7, 8, 9.
The total number of possible numbers that meet the condition is 9 * 9 * 9 * 9 * 9 = 59,049 (each digit has 9 choices).
The total number of possible five-digit natural numbers is 9 * 10 * 10 * 10 * 10 = 90,000 (the first digit can't be zero, so there are 9 choices, while the remaining digits can be any number from 0 to 9).
The probability is given by the number of favorable outcomes (numbers that meet the condition) divided by the number of possible outcomes:
Probability = 59,049 / 90,000 ≈ 0.6561