Question 1182760
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The arrangements must not have two odd numbers next to each other.  With three odd numbers and three even numbers, that means the six numbers must alternate between even and odd.<br>
So in terms of even and odd numbers, the arrangement must be of the form<br>
ABABAB<br>
The first number can be any of the 6.
The second number must be one of the 3 of the opposite parity.
The third must be one of the remaining 2 that have different parity than the second.
The fourth must be one of the remaining 2 that have different parity than the third.
The fifth must be the 1 that has different parity than the fourth.
There is only 1 left for the sixth position.<br>
Total number of arrangements with alternating even and odd: 6*3*2*2*1*1 = 72.<br>
ANSWER: 72<br>