Question

A password is 4 characters long and must consist of 3 letters and one number. If letters cannot be repeated and the password must end with a number, how many possibilities are there?

Answer 1

26 x 25 x 24 x 10 = 156,000 possibilities

Answer 2

Answer would be 156,000.

Explanation:

A password is 4 characters long and must consists of 3 letters and one number.

Alphabets = 26 letters ( A to Z )

numbers = 10 ( 0 to 9 )

If no repeats are allowed for letters and the password must end with a number. We use the formula :

`P(n,r)= (n!)/((n-r)!)`

n = object (26)

r = sample (3)

`n=(26!)/((26-3)!)* 10`

`n=(26* 25* 24* 23!)/((26-3)!)* 10`

n = 15,600 × 10 = 156,000

There are 156,000 possibilities.