How many even 2 digit numbers can be formed from the numbers 3,4,5,6,7? The digits cannot repeat (you can't have 44 or 66 for example). I know the answer to this is 8, because I just wrote them all out and then removed the ones that repeated digits, but I need a way to find this using a formula, like P(n,k) or something. What formula could be used to find this?
[Math] How many 2 digit even numbers can be formed from these numbers
combinatoricsdiscrete mathematicspermutations
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Best Answer
There is no formula for this, here. Because you have specified the digits and a way to understand this intuitively is-
$__ __ $
Suppose these dashes are the two digits.
So, in order for a number to be even, the last digit should be $0$ or $2,4,6,8$. So second digit can be $4$ or $6$ from your specified numbers. And the digit cannot be repeated, so there are $3+1=4$ digits left for the first place. So by multiplication principle, $$4\cdot 2=8$$ is the answer.