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
• B. 671
• C. 716
• D. 761

Answer 1

The correct option is B 671

Least digit used = 4
$\therefore$ We can use 4,5,6,7,8,9. But remember that at least one 4 must be used.
------(4 blanks)
$1^{st}$ blank can be filled in 6 ways.
$2^{nd}$ blank can be filled in 6 ways.
$3^{rd}$ blank can be filled in 6 ways.
$4^{th}$ blank can be filled in 6 ways.
4 blanks can be filled in $6^4$ 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)
$\therefore 5^4$ ways (no 4 at all)
$\therefore$ Ans =$6^4-5^4$ (at least one 4)
=671