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) $=671$.