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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.)

 Apr 11, 2022
 #1
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+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

 Apr 11, 2022
 #3
avatar+117819 
+1

Guest, it is only 5 digits and the first one must be 9.

Melody  Apr 12, 2022
 #2
avatar+117819 
+1

chose 4 digits that are less then 9

8,7,6,5,4,3,2,1,0

9C4=126

 

I get 126.

 Apr 12, 2022

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