easy

how many three digit numbers are there with no digit repeated


The answer is 648.

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1 solution

Aditya Raut
Jul 15, 2014

Let the 3 digit number be A B C \color{#D61F06}{\text{Let the 3 digit number be }} \overline{ABC}

Then, there are 9 9 choices for digit A A because it can be anything out of ( 1 , 2 , 3 , . . . , 9 ) (1,2,3,...,9) ( 0 is not allowed as A because then number is not 3 digit)

Then, there are again 9 9 choices for digit B B , because you can't take the digit which was chosen for A A but you can take 0 0 this time, giving 9 9 choices,

Now, for C C , you have 8 8 choices because 2 out of the total 10 10 digits have already been chosen.

Thus by the M u l t i p l i c a t i o n \color{#3D99F6}{Multiplication} R u l e \color{#20A900}{Rule} , there will be 9 × 9 × 8 = 648 9\times 9\times 8= \boxed{\color{#69047E}{648}} numbers.

how about if you start at the ones digit up to the hundreds. you can have 7 x 9 x 10. Isn't this possible?

edmund letaba - 6 years, 10 months ago

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That is not possible. If you chose 0 on digit C or B, then digit A will have 8 options instead of 7.

Esrael Santillan - 6 years, 10 months ago

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