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| Math Central | Quandaries & Queries |
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Question from Rob: If there is a 4 digit passcode with only 6 punch in symbols, how many possibilities are there and what are they? |
Hi Rob.
It depends on whether duplicates are allowed. For example, is Y, X, LT, X allowed?
It also depends on whether order is important. Is Y, X, LT, RT different from RT, Y, X, LT?
Assuming the answers to both question are Yes, you have 6 choices for each of the four positions, so the number of possibilities is 6 x 6 x 6 x 6.
If duplicates are not allowed, then you have 6 choices for the first symbol, 5 for the next, etc. So the number of possibilities is 6 x 5 x 4 x 3.
If order is not important, you have to weed out duplicates. The number of duplicates is the number of ways of arranging 4 things: 4 x 3 x 2 x 1 . So you would divide the number of possibilities by 24.
Cheers,
Stephen La Rocque.
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