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##### Suppose we have a door with a keypad lock; the lock has five buttons

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Suppose we have a door with a keypad lock; the lock has five buttons (labelled 1, 2, 3, 4, and 5) and a code for the lock is six digits long.

(a) What is the total number of possible combinations for the door? (b) What does the Pigeonhole Principle tell us about the possible combinations? (c) How many combinations are there that avoid having the same digit twice in a row? (d) Suppose we select a combination for the door at random. What is the probability that it consists only of odd numbers?

Oct 19th, 2017

If order is not important, for example 135 is the same as 351, then you want the number of ways of choosing 3 things from 6 things. This is called "6 choose 3" and it is written

If order is important then these are called permutations. You have 6 choices for the first digit, 5 choices for the second digit and 4 choices for the third digit so you have

Apr 21st, 2015

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Oct 19th, 2017
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Oct 19th, 2017
Oct 19th, 2017
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