One of the standard telephone numbers for directory assistance is 555−1212. How many different permutations of this telephone number are possible?.

7!/(3!2!2!) = 210

Ah, the magical world of telephone numbers! Let's see, we have 10 digits to work with: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Since the first digit cannot be zero, we have 9 options for the first digit.

For the remaining 7 digits, any number from 0 to 9 can be chosen, so we have 10 options for each digit.

Therefore, the total number of different permutations of the telephone number is:

9 * 10 * 10 * 10 * 10 * 10 * 10 * 10 = 9,000,000

That's a whole lot of number combinations! Dial away, my friend!

To find the number of different permutations of the telephone number 555-1212, we need to consider the digits and the dash separately.

There are 7 digits in the telephone number: 5, 5, 5, 1, 2, 1, and 2.
Since the digit 5 appears three times and the digits 1 and 2 appear twice each, we need to calculate the number of permutations considering the repeating digits.

First, let's consider the digits 1 and 2, which appear twice each.

The number of permutations of the digits 1 and 2 is given by the factorial of the number of digits, divided by the factorial of the number of repetitions. This can be calculated as:

(2!)/(2!) = 1.

Now, let's consider the digit 5, which appears three times.

The number of permutations of the digit 5 is given by the factorial of the number of digits, divided by the factorial of the number of repetitions. This can be calculated as:

(3!)/(3!) = 1.

Now, we can multiply the number of permutations for each group of digits:

1 * 1 * 1 = 1.

Therefore, there is only 1 possible permutation of the telephone number 555-1212.

To find the number of different permutations of the telephone number 555-1212, we need to count the number of ways we can arrange its digits.

The telephone number consists of 4 digits (5, 5, 1, 2) and 3 hyphens (-). We will treat the hyphens as distinct digits for this calculation. Therefore, we have a total of 7 digits to arrange.

To determine the number of permutations, we need to calculate 7 factorial (7!), which is the product of all positive integers from 7 down to 1.

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

Hence, there are 5040 different permutations of the telephone number 555-1212 possible.