Question

For your own safety, the bank representative says that the following characteristics of PIN numbers are prohibited: ​​(1) all four digits identical,​(2) sequence of consecutive ascending or descending digits, such as 0123 or 3210, ​(3) any sequence starting with 19 or 20 (birth years). ​​How many sequences would NOT be permitted?

Answer 1

Total = N(1) +N(2)+N(3) = 10+14+200 = 224 sequences

224 sequences would NOT be permitted.

Explanation:

1) all four digits identical

Number of possible PIN with all four digits identical N(1) = 1×1×1×10 = 10 possible PIN

2) sequence of consecutive ascending or descending digits N(2) = 14

Only Ascending starting with 0,1,2 = 3

only descending for 7,8,9 = 3

and both for 3,4,5,6 = (2×4)

Total = 3+3+(2×4) = 14

3) any sequence starting with 19 or 20 (birth years

N(3) = 2 × 1×1×10×10 = 2×100 = 200

N(3) = 200

(Note : 100 possible ways for each of 19 or 20s)

Total = N(1) +N(2)+N(3) = 10+14+200 = 224

224 sequences would NOT be permitted.