Matt is asked to write the numbers from 1 to 10 in order, but he forgets how to count. He writes a permutation of the numbers \{1,2,3 \ldots, 10\} across his paper such that:
(a) The leftmost number is 1 .
(b) The rightmost number is 10 .
(c) Exactly one number (not including 1 or 10) is less than both the number to its immediate left and the number to its immediate right.
How many such permutations are there?