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.Com
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)   (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
RELATED QUESTIONS

Find how many different odd 4-digit numbers less than 4000 can be made from the digits... (answered by Edwin McCravy)
(i) Find how many different numbers can be formed using 4 of the digits 1, 2, 3, 4, 5, 6 (answered by ikleyn)
from the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, four different numbers are selected to... (answered by ikleyn)
From the numbers 1,2,3,4,5,6,7,8, and 9, four different numbers are selected to form a... (answered by ikleyn)
From the numbers 1,2,3,4,5,6,7,8, and 9, four different numbers are selected to form a... (answered by ikleyn)
Find how many different odd 4-digit numbers less than 4000 can be made from the digits... (answered by Edwin McCravy)
How many odd 6-digit pin numbers can be made from the digits... (answered by edjones,josmiceli)
A 4-digit pin number is to be created using the digits 0 through 9. The first digit must (answered by ikleyn)
How many four-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, if the... (answered by mccravyedwin,Edwin McCravy,ikleyn)