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Question

The number of 4-digit numbers that can be formed by using the digits 1,2,3,4,5,6,7,8 and 9 such that the At least digit used is 4, when repetition of digits is allowed, is

A
617
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B
671
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C
716
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D
761
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Solution

The correct option is B 671
Least digit used = 4
We can use 4,5,6,7,8,9. But remember that at least one 4 must be used.
------(4 blanks)
1st blank can be filled in 6 ways.
2nd blank can be filled in 6 ways.
3rd blank can be filled in 6 ways.
4th blank can be filled in 6 ways.
4 blanks can be filled in 64 ways. But out of these, some may contain no 4 at all. Let us find them.
-------(4 blanks)
Each blank can be filled in 5 ways (by 5, 6, 7, 8, or 9)
54 ways (no 4 at all)
Ans =6454 (at least one 4)
=671

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