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Different Digital Clock

Stage: 3 Short Challenge Level: Challenge Level:1
See all short problems arranged by curriculum topic in the short problems collection

A digital clock uses two digits to display hours, two digits to display minutes and two digits to display seconds, e.g. $10$:$23$:$42$.

How many times between $10$:$00$:$00$ and $11$:$00$:$00$ on the same morning are all six digits different?
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.