A computer password is composed of five characters. If each character must be a letter (A - Z), then how many different passwords can be created which use different vowels for the first three characters And different consonants for the last two characters? (Note: The vowels are A, E, I, O, and U.)
A) 253
B) 7542
C) 25200
D) 589920
E) None of the above.

Question

Quizplus · Accepted Answer

There are 5 vowels and we need to choose 3 different ones for the first three characters, which can be done in 5P3 = 60 ways. There are 21 consonants and we need to choose 2 different ones for the last two characters, which can be done in 21P2 = 420 ways. Therefore, the total number of different passwords is 60 * 420 = 25200.

A Computer Password Is Composed of Five Characters