A passcode to unlock a security door consists of three digits followed by 2 letters. How many passcodes are possible satisfying each of the following conditions?

Question

a) There are no restrictions. b) No digit is used more than once. c) No vowel (A, E, I, O, or U) is used.

Answer 1

10x10x10 x 26x26= 1,000 x 676, for 3 digits followed by 2 letters

= 676,000 passcodes if no restrictions

10x9x8x26x26 = 486,720 if no digit is used more than once

10x10x10x21x21 = 441,000 if no vowels are used

26-5 vowels leave 21 letters.