Arrangements of 1 to 7 with evens never touching

Count the orderings of the numbers $1,2,3,4,5,6,7$ in which no two even numbers sit next to each other.

$1440$. Place the four odd numbers first ($4!$ ways); they create $5$ gaps, and the three evens must go in three different gaps: $\binom53=10$ choices of gaps and $3!$ orders. Total $24\cdot10\cdot6=1440$.