SOLUTION: How many three-digit counting numbers are there that are less than 300 such that all the digits are even?

Question 67089This question is from textbook Advanced mathematics
: How many three-digit counting numbers are there that are less than 300 such that all the digits are even? This question is from textbook Advanced mathematics

Answer by Zoop(21) (Show Source): You can put this solution on YOUR website!
Wierd---I thought I had solved this one already, but for some reason, I can't find it. Anyway, here's how to do it.
There is only 1 possibility for the first digit of any of the numbers, as no 3-digit number with an even first digit is underneath 300 unless the first digit is 2. Therefore, we take 1 as the first term.
For the second one, it could be 2,4,6, or 8. So there are 4 choices, as there are for the third term too.

Therefore, we have 16 counting numbers less than 300 that have all even digits.
If you'd like a list of the numbers:
222
224
226
228
242
244
246
248
262
264
266
268
282
284
286
288
Done. =)
-Zoop
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