Question

A newspaper ad includes a telephone number 1-555-dial vsw. How many seven letter arrangements are possible for the phone number using the 26 letters of the alphabet of no letter is ised more than once? Express your answer using scientific notation.

Answer 1

There are 3,752,400 possible seven-letter arrangements for the phone number.

Step-by-step explanation:

To determine the number of seven-letter arrangements for the phone number, we need to consider that no letter can be used more than once.

Since there are 26 letters in the alphabet, we have 26 choices for the first letter, 25 choices for the second letter, 24 choices for the third letter, and so on.

Therefore, the total number of arrangements is:

26 x 25 x 24 x 23 x 22 x 21 x 20 = 26! / (26-7)!

Using a calculator, we can simplify this expression to:

26 x 25 x 24 x 23 x 22 x 21 x 20 = 3,752,400

So, there are 3,752,400 possible seven-letter arrangements for the phone number.

Answer 2

Let u be the set of all words containing 7 letters(26 letters to the power 7)