combination

I was playing with padlock that require number combination instead of key to unlock it. i found this padlock in my house and i want to use it. so I had been trying each combination till I get the right one but then I wonder how many combination do I have to try?

how many combination can be made for 3 slots with each having numbers 0 to 9 that can be put in?
easy. we all know the answer without even calculating it right? this is the usual type of padlock used for combination.

the padlock that im playing with is a lil bit different. its not like the usual 3 slots with number 0 to 9 for each slots but this one has number 0 to 9 with each of them can be put  up or down. so in other word, how many combination can be made from ten slots with each of the slots can be put X or O? I cant put them into words in a better way. hope you guys understand it.

answer

so for the first type of padlock the answer is simple, 1000 combination. you can make 999 numbers plus 000 which make it 1000 combinations. here's how you calculate it. 10C1 x 10C1 x 10C1 which you get 1000. easy enough.

the second one...since each number has the option either up or down and we have number 0 to 9 which is 10 in total, calculation for it would be (2C1)^10. the answer is 1024. I'm actually surprised that even though the lock looks simple it actually has more combination than the ordinary padlock.

Dazdinggor!!! a sketch of voljin the witch doctor