Counting how many numbers have repeated digits How many numbers are there in all from $6000$ to $6999$ (both $6000$ and $6999$ included) having at least one of their digits repeated ?
(a) $216$
(b) $356$
(c) $496$
(d) $504$

Hint: try counting the numbers that don't have any of their digits repeated, and subtract those from the total.  You should get answer (c).

 we have $1000 - {}_9P_3 =1000 - 9 \times 8 \times 7 = 496$

