Problem
COM-B1-M02-P018 Even Numbers in Even Positions
#18
★★★☆☆ Level 3 of 5
How many permutations of \(1,2,\ldots,7\) have the even numbers exactly in even positions?
There are three even positions and three even numbers.
The even numbers \(2,4,6\) can be placed in positions \(2,4,6\) in \(3!\) ways. The odd numbers \(1,3,5,7\) occupy the remaining positions in \(4!\) ways. Answer: \(3!\cdot4!=144\).
Position restrictions without inclusion-exclusion.