Question

~~How many arrangements are there of the digits 1, 2, 3, 4, 5, if the odd digits must be in ascending order?

I do not know whether this question involves permutations only.

Answer 1

There 120 arrangements of the digits ignoring the order of the odd digits.

There are 6 ways of arranging 1, 3 and 5: 135 153 315 351 513 531, but only one of these keeps them in ascending arithmetic order. Therefore we need to divide 120 by 6=20 to get the number of arrangements where the odd digits are in order. Solution: 20 arrangements.