Answer: a) 100,000 b) 200 c)65610
Explanation:
a) for a 5 digit number. Each digit have 10 possible values that is 0 - 9
Therefore, number of possible unique 5 digit number possible is
10×10×10×10×10= 100,000
b) For it to start begin with either 023 and 003.
- the first digit must be 0 (1 possible value)
- 2nd digit must be 2 or 0 (2 possible values)
- 3rd digit must be 3 (1 possible value)
- 4th and 5th can be filled with any digit (10 × 10 possible values)
Which gives
1×2×1×10×10= 200
c) no two adjacent digits are the same that is no two digits that follows each other are the same.
In this case only one digit have 10 possible values.
The other four digits have 9 possible values each.
Which gives:
10×9×9×9×9= 10×9^4 = 65610
