Question

John used digits from 0 to 6 to create a three-digit PIN code. He forgot his PIN code. He remembers that his code contains different ascending digits. What is the maximum number of combinations John has to check to find his PIN code.

Answer 1

35 combinations

Explanation:

The first digit cannot be 5 or 6 (Since the digits could not be in ascending order if that was the case).

If the first digit is 4, there is 1 possibility:

(4, 5, 6)

If the first digit is 3, there are 3 possibilities:

(3, 4, 5) (3, 4, 6) (3, 5, 6)

If the first digit is 2, there are 6 possibilities:

(2, 3, 4) (2, 3, 5) (2, 3, 6) (2, 4, 5) (2, 4, 6) (2, 5, 6)

If the first digit is 1, there are 10 possibilities :

(1, 2, 3) (1, 2, 4) (1, 2, 5) (1, 2, 6) (1, 3, 4) (1, 3, 5) (1, 3, 6) (1, 4, 5) (1, 4, 6) (1, 5, 6)

If the first digit is 0, there are 15 possibilities:

(0, 1, 2) (0, 1, 3) (0, 1, 4) (0, 1, 5) (0, 1, 6) (0, 2, 3) (0, 2, 4) (0, 2, 5) (0, 2, 6) (0, 3, 4) (0, 3, 5) (0, 3, 6) (0, 4, 5) (0, 4, 6) (0, 5, 6)

Therefore, he would need to try at most 35 combinations.