Question

I know a) is 100

Confused about b) I got 81 but its wrong


Need an explanation along with answer

Answer 1

45

Explanation:

At this point, b) is basically asking for how many two digits numbers have a greater digit on the right from 0-9, because we already know the other two digits in the four-digit pin.

01-09 has 9 poissibilites.

12-19 has 8 possibilites.

23-29 has 7 possibilites.

34-35 has 6 possibilites.

45-49 has 5 possibilites.

56-59 has 4 possibilities.

67-69 has 3 possibilities.

78-79 has 2 possibilities.

89 has 1 possibility.

90-99 has 0 possibilities.

9+8+7+6+5+4+3+2+1+0=45 possibilities.

Answer 2

• A) 100 codes, B) 45 codes

Explanation:

Part A

Each of the digits 3 and 4 can get numbers 0 through 9, in total 10 options per each digit:

• 10*10 = 100 combinations

Part B

The two- digit combinations with the last digit being larger has the following cases:

• Digit 4 is 9, then digit 3 can get 0 through 8 ⇒ 9 options,
• Digit 4 is 8, then digit 3 can get 0 through 7 ⇒ 8 options,
• ...
• Digit 4 is 1, then digit 3 can get 0 ⇒ 1 option

Total number of possibilities:

• 9 + 8 + 7 + ... + 1 = (9 + 1)*9/2 = 10*9/2 = 45