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?

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

224 sequences would NOT be permitted.

Step-by-step 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.