SOLUTION: How many 3-digit numbers can be formed from the set 0-9 if repetitions are not allowed and the number must be divisible by a)10? b)25?

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Question 1116174: How many 3-digit numbers can be formed from the set 0-9 if repetitions are
not allowed and the number must be divisible by
a)10?
b)25?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


(a) divisible by 10:

The number must be of the form AB0. 1 choice for the units digit (0); 9 choices for A (anything but 0); 8 choices for B (anything but 0 or A).
Total: 1*9*8 = 72

(b) divisible by 25:

Three possibilities for the last 2 digits: 25, 50, or 75

In each of the three cases, there are 8 choices for the first digit, making a total of 24.

Answers: (a) 72; (b) 24

Answer by ikleyn(52890) About Me  (Show Source):
You can put this solution on YOUR website!
.
For case b) I have another solution and different answer. 

    The two last digits must be "25", or "50" or "75"  (00 does not work, since repetitions are not allowed).


    If the last two digits are "25", then the first digit can be any of only 7 digits  1, 3, 4, 6, 7, 8, 9.


    If the last two digits are "50", then the first digit can be any of 8 digits  1, 2, 3, 4, 6, 7, 8, 9.


    If the last two digits are "75", then the first digit can be any of only 7 digits  1, 2, 3, 4, 6, 8, 9.


    In all, there are  7 + 8 + 7 = 22 opportunities for the first digit and, correspondingly, 22 three-digit numbers

    satisfying the condition.