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Question
How many three-digit numbers are there with 3 in the unit place?
without repetition
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Solution
The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
A three-digit number has 3 digits 1’s, 10’s and 100’s place.
The unit place is (filled by 3) filled in one way.
After filling the unit place since the digit ‘0’ is there
We have to fill the 100’s place.
Now to fill the 100’s place we have 8 digits (excluding 0 and 3)
So 100’s place can be filled in 8 ways.
Now to fill the 10’s place we have again 8 digits (excluding 3 and any one of the number)
So 10’s place can be filled in 8 ways.
∴ Number of 3 digit numbers with ‘3’ in unit place = 8 × 8 × 1 = 64
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