The number of 4 digit number that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contains digit 1 is

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1225

1252

630

750

answer is D.

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Detailed Solution

The number of 4 digits number that can be form from the digits 0,1,2,3,4,5,6,7 so that each number contains digit 1 is Given that number is of 4 digits so the first digit can't be 0.
Let (i) first digit is (1).
(ii) first digit is not 1
(i) First digit is 1
We pick 3 digits in order out of the remaining 7.6.5=210 possibilities.
(ii) First digit is not 1
There are 6 ways to choose the first digit (2,3,4,5,6,7), 3 ways to place the digit 1 (hundreds, tens, ones)
and 6.5 ways to choose the other digits So 6.3.6.5=540 possibilities
Then, total possibilities are 210+540=750
750 possibilities to choose the number that to each number contains digit 1.

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