A push-button padlock - Math Central

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Question from Vince:

Hi,

I have a push-button padlock using ten buttons (1-2-3-4-5-6-7-8-9-0).
Five digits must be pushed in order to open the lock.
Each digit can only be used once.
Order is not supposed to matter.

How many different possible combinations? And what are they?

Hi Vince,

This is the number of ways of choosing 5 objects from 10 objects. Mathematicians call this number 10 choose 5. You can find an expression for n choose k in Penny's response to an earlier question.

Google will calculate 10 choose 5 for you. If you input 10 choose 5 then Google responds with 10 choose 5 = 252. As for listing them I can get you part way. The combinations section of the Amazing Mathematical Object Factory will generate n choose k for n = 10 and k = 5 but it stops at 200 combinations. I don't know of an online facility that will generate all 252 for you.

Harley

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