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.)

Guest Apr 11, 2022

#1**+1 **

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**

Guest Apr 11, 2022