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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?

Respuesta :

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

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 :

[tex]P(n,r)= \frac{n!}{(n-r)!}[/tex]

n = object (26)

r = sample (3)

[tex]n=\frac{26!}{(26-3)!}\times 10[/tex]

[tex]n=\frac{26\times 25\times 24\times 23!}{(26-3)!}\times 10[/tex]

n = 15,600 × 10 = 156,000

There are 156,000 possibilities.