Coin Brilliant

Odds of randomly/blindly being able to choose 10 numbered coins in numerical order?
Hi! I need the expertise of a mathematician on this question please … if I have 10 coins marked from one to ten each, put them a hat, and shake them around, what are the odds I would (without looking) be able to pull each coin out in exact numerical sequence? I know that my chances of pulling out coin #1 on the first try would be one in ten (just a simple layer of the equation). But what are the chances of getting them all in order? Is it one in a million? Billion? More? I’m not sure how the multiplication would work on this. I’ll later explain why I need the statistic (it’s pretty cool, actually — for a teaching project). If any brilliant person out there could let me know how to calculate this answer, I’d appreciate it!! A detailed explanation would be extra helpful. Thanks. : )
It’s simpler than you think. As you stated, your odds of pulling #1 on the first try are one in ten. Then, your odds of pulling out #2 on the second try are one in nine. Odds of #3 on the third: one in eight, and so on. So the chance of pulling all ten in a row is 1/10!, or 1/(10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1)
Multiply it out, and you have a 1 in 3,628,800 chance of pulling off this particular feat.
Make the penny a dollar coin
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