Question

A man and a woman meet at a restaurant. After a long conversation, they agree to have dinner the next day if the man remembers to call the woman to confirm the date. The next morning the man discovers that he can remember the digits in her number (2, 3, 4, 5, 6, 7, and 8), but he has completely forgotten their order. If he decides to arrange the seven digits in random order and dial every combination, what are the chances that any given number will be her phone number?

Answer 1

The probability of dialing the correct phone number with the remembered digits in a random order is 1 in 5040, because there are 5040 unique permutations of the 7 digits.

Step-by-step explanation:

The question at hand involves calculating the probability that any given number dialed will be the woman's actual phone number, given that a man can remember the digits but not their order. Since there are 7 unique digits, the total number of possible arrangements or permutations of these 7 digits is 7 factorial (7!). The factorial notation, denoted as 'n!', means the product of all positive integers up to 'n' (e.g., 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040). Therefore, the probability of dialing the correct number on any given attempt is 1/5040, as there is only one correct arrangement of the digits that would match the woman's phone number.