Question

How many four digit numbers contain the digit pattern 35 at least once and only once?
Explain how you got it.

Answer 1

at least once would be:
ab35, where a is 1-9 and b is 0-9 (90 possibilities)
a35b, where a is 1-9 and b is 0-9 (90 possibilities)
35ab, where a and b are 0-9 (100 possibilities)

so the answer is 280. This assumes leading zeros are not allowed.

Answer 2

exactly once would be the same, except "ab" can't be exactly "35" in the first or last case, which only eliminates 2 possibilities, putting the answer at 278.

Answer 3

is it 278or 28-

Answer 4

280*

Answer 5

280 is "at least once." 278 is "exactly once." you asked for both.

Answer 6

or at least, that's how I read it. :-)

Answer 7

right right, thanks!