Using all digits from 0 to 9, how many 5 digit numbers can be formed? Repetition of digits is allowed.
105
9 × 8 × 7 × 6 × 5
90,000
95
Method 1:
We have to fill 5 slots
1st can be filled with any digit from 1 to 9 (not 0): so 9 options
Rest of the slots can be filled by any of the 10 digits from 0 to 9: so 10 options for each
So, total numbers: 9*10*10*10*10 = 90,000
Method 2:
The trick is to realize that a number can not start with a zero.
Now, there are 105 ways in which the digits 0-9 can be chosen for the five places of a five digit number. Out of these, 104 start with zero (once we start with 0, there are only 4 slots to fill, where we have 10 choices each).
So, the number of possible five digit numbers is
105−104=90000
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