Permu is the guy
If each digit is used exactly once, how many ways can the 5 digits above be arranged so that and are not adjacent?
The answer is 72.
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1 solution
The number of ways the five digits can be rearranged is: 5!=120.
For now, let us consider the digits 2 and 4 as one which renders us 4 digits, the number of ways the four digits can be rearranged is: 4!=24.
To calculate how many ways 4 and 2 are adjacent, we multiple the number we obtained above: 24 * 2 =48.
All that's left is trivial, simply subtract them: 120 -48 = 72.