Creating Even #s Out of Lists of #s

The # of ways to create an even # when given a list of #s is tricky when ZERO is involved


Example


How many 4 digit even #s can be made out of the following digits: 2, 3, 4, 8, 9, 0, without repetition?

To answer this question you must split the question into two cases:

ending in 0 and ending in an even #

ending in 0

  5   4  x  3  x 1   = 60

the first blank has a five because once the 0 is used you have 5 #s that could go in the first spot

 

ending in 2, 4, or 8

 4   x  4  x  3  x 3   = 144

the first blank is a 4 because although there are 5 #s left for that spot after one of 2, 4, or 8 are used in the last spot, the zero cannot be placed there if you want a four digit #, ie: 0298 is only a three digit #


You would then add these #s together to find how many 4 digit even #s can be created.

204

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Tomorrow's blog will show a way to do the binomial expansion quicker using symettry.

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Dec 11, 2012 Posted by: Tom MacFarlane
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