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
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 x 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 = 144the 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.
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Tomorrow's blog will show a way to do the binomial expansion quicker using symettry.
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