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?

playbiEzJ

playbiEzJ

Answered question

2022-11-25

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 & Explanation

hayaniqWf

hayaniqWf

Beginner2022-11-26Added 10 answers

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 ) = 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.

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