How many sequences of 6 digits x_{1}, x_{2}, ... , x_{6} can we form, given the condition that no two adjacent x_{i} have the same parity? Leading zeroes are allowed. (Parity means 'odd' or 'even'; so, for example, x_{2} and x_{3} cannot both be odd or both be even.)

Mathgenius Dec 8, 2018

#1**+1 **

well it's clear that among your x's 3 must be even and 3 must be odd.

The evens can occupy either slots 1,3,5 or slots 2,4,6

There are 3! = 6 ways you can arrange them in those slots.

The odds will occupy the remaining slots and again there are 6 ways to arrange them.

So in total there are 6*6=36 ways to arrange your x's as described.

Rom Dec 8, 2018

#1**+1 **

Best Answer

well it's clear that among your x's 3 must be even and 3 must be odd.

The evens can occupy either slots 1,3,5 or slots 2,4,6

There are 3! = 6 ways you can arrange them in those slots.

The odds will occupy the remaining slots and again there are 6 ways to arrange them.

So in total there are 6*6=36 ways to arrange your x's as described.

Rom Dec 8, 2018