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:

Answer would be 156,000.

Step-by-step 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 :

$P(n,r)= \frac{n!}{(n-r)!}$

n = object (26)

r = sample (3)

$n=\frac{26!}{(26-3)!}\times 10$

$n=\frac{26\times 25\times 24\times 23!}{(26-3)!}\times 10$

n = 15,600 × 10 = 156,000

There are 156,000 possibilities.