CAYLEY 2014 Problem 22

A five-digit positive integer is created using each of the odd digits 1,3,5,7,9 once so that

  • the thousands digit is larger than the hundreds digit,
  • the thousands digit is larger than the ten thousands digit,
  • the tens digit is larger than the hundreds digit, and
  • the tens digit is larger than the units digit.

How many such five-digit positive integers are there?

Answer Choices
A. 12
B. 8
C. 16
D. 14
E. 10