How many five-digit numbers have distinct digits which are decreasing from left to right, and that start with a digit of 9? (For example, 96531 is such a number.)
There are:
(9, 8, 7, 6, 5) , (8, 7, 6, 5, 4) , (7, 6, 5, 4, 3) , (6, 5, 4, 3, 2) , (5, 4, 3, 2, 1) , (4, 3, 2, 1, 0) , >Total = 6 combinations
(4, 3, 2, 1, 0) ==1 permutation
(5, 4, 3, 2, 1)==5 permutations
(6, 5, 4, 3, 2)==15 permutations.
(7, 6, 5, 4, 3) ==35 permutations.
(8, 7, 6, 5, 4) ==70 permutations.
(9, 8, 7, 6, 5) ==126 permutations.
{1 + 5 + 15 + 35 + 70 + 126} ==252 permutations
