Question

How many three digit even positive number can be formed from the digits 0 to 9 ,if the digit can be repeate?d

Answer 1

SOLUTION

TO DETERMINE

The number of three digit even positive number can be formed from the digits 0 to 9 if the digit can be repeated

EVALUATION

Here we have to find three digit number

So it has three places, unit place, ten place, hundred place

Now we have the digits 0 to 9

Since the number is even

So the unit place must be one of 0, 2, 4, 6, 8

So unit place can be selected in 5 ways

Next ten place can be any one from the digits 0 to 9

So ten place can be selected in 10 ways

Since the number is three digit

So hundred place can not be 0

So hundred place can be any one from the digits 1 to 9

So hundred place can be selected in 9 ways

So the required number of three digit even positive number can be formed from the digits 0 to 9 is

$= 5 \times 10 \times 9$

$= 450$

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Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

Here we have to find three digit number

So it has three places, unit place, ten place, hundred place.

Now we have the digits 0 to 9

Since the number is even

So the unit place must be one of 0, 2, 4, 6, 8

So unit place can be selected in 5 ways

Next ten place can be any one from the digits 0 to 9

So ten place can be selected in 10 ways

Since the number is three digit

So hundred place can not be 0

So hundred place can be any one from the digits 1 to 9

So hundred place can be selected in 9 ways

• So the required number of three digit even positive number can be formed from the digits 0 to 9 is

→ 5×10×9

→ 450