SOLUTION: how many different four digit pin numbers can be made from the digits 2,3,4,5 A=if the number is less than 3000 B=if the number must be divisable by 5 C=if the number must be e

Algebra ->  Permutations -> SOLUTION: how many different four digit pin numbers can be made from the digits 2,3,4,5 A=if the number is less than 3000 B=if the number must be divisable by 5 C=if the number must be e      Log On


   

Question 550823: how many different four digit pin numbers can be made from the digits 2,3,4,5
A=if the number is less than 3000
B=if the number must be divisable by 5
C=if the number must be even
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
how many different four digit pin numbers can be made from the digits 2,3,4,5
A=if the number is less than 3000
B=if the number must be divisable by 5
C=if the number must be even
Are you allowing repetitions of digits in pin numbers like 2335, 2244, or 5555?
I'll do it both ways:

A=if the number is less than 3000

If repetitions are allowed,             If repetitions are NOT allowed 
Choose the 1st digit 1 way, as "2".     Choose the 1st digit 1 way, as "2".
Choose the 2nd digit 4 ways.            Choose the 2nd digit 3 ways.
Choose the 3rd digit 4 ways.            Choose the 3rd digit 2 ways.
Choose the 4th digit 4 ways.            Choose the 4th digit 1 way.
Answer 1×4×4×4 = 64 ways.               Answer 1×3×2×1 = 6 ways.

B=if the number must be divisable by 5
If repetitions are allowed,             If repetitions are NOT allowed 
Choose the 4th digit 1 way, as "5".     Choose the 4th digit 1 way, as "5".
Choose the 1st digit 4 ways.            Choose the 1st digit 3 ways.
Choose the 2nd digit 4 ways.            Choose the 2nd digit 2 ways.
Choose the 3rd digit 4 ways.            Choose the 3rd digit 1 way.
Answer 1×4×4×4 = 64 ways.               Answer 1×3×2×1 = 6 ways.

C=if the number must be even
If repetitions are allowed,             If repetitions are NOT allowed 
Choose the 4th digit 2 ways, (2 or 4).  Choose the 4th digit 2 ways, (2 or 4).
Choose the 1st digit 4 ways.            Choose the 1st digit 3 ways.
Choose the 2nd digit 4 ways.            Choose the 2nd digit 2 ways.
Choose the 3rd digit 4 ways.            Choose the 3rd digit 1 way.
Answer 2×4×4×4 = 128 ways.              Answer 2×3×2×1 = 12 ways.

Edwin