Mathematics - Permutation & Combination Question with Solution | TestHub

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)

$1^{\text{st }}$ blank can be filled in 6 ways.

$2^{\text{nd }}$ blank can be filled in 6 ways.

$3^{\text{rd }}$ blank can be filled in 6 ways.

$4^{\text{th }}$ blank can be filled in 6 ways.

$\therefore 4$ 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)

∴ Ans $=6^4-5^4$ (at least one 4)

$=671$.