+0

# Question #3

+1
926
5
+1211

We call a number a descending number if each digit is strictly smaller than the digit that comes before it. For example, 863 is a descending number. How many 3-digit descending numbers are there?

Mar 11, 2018

#1
+1

Numbers beginning with 2 =2C2 =1

.......................................3 =3C2 =3

.......................................4 =4C2 =6

.......................................5 =5C2 =10

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,6 =6C2 =15

.......................................7 =7C2 =21

.......................................8 =8C2 =28

.......................................9 =9C2 =36

There are a total of = 120 descending numbers

Mar 12, 2018

#1
+1

Numbers beginning with 2 =2C2 =1

.......................................3 =3C2 =3

.......................................4 =4C2 =6

.......................................5 =5C2 =10

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,6 =6C2 =15

.......................................7 =7C2 =21

.......................................8 =8C2 =28

.......................................9 =9C2 =36

There are a total of = 120 descending numbers

Guest Mar 12, 2018
#3
+1211
+1

Thank you! You are correct!

Lightning  Mar 13, 2018
#4
+1211
+1

Thank you! You are correct!

Lightning  Mar 13, 2018
#2
0

{9, 8, 7} | {9, 8, 6} | {9, 8, 5} | {9, 8, 4} | {9, 8, 3} | {9, 8, 2} | {9, 8, 1} | {9, 8, 0} | {9, 7, 6} | {9, 7, 5} | {9, 7, 4} | {9, 7, 3} | {9, 7, 2} | {9, 7, 1} | {9, 7, 0} | {9, 6, 5} | {9, 6, 4} | {9, 6, 3} | {9, 6, 2} | {9, 6, 1} | {9, 6, 0} | {9, 5, 4} | {9, 5, 3} | {9, 5, 2} | {9, 5, 1} | {9, 5, 0} | {9, 4, 3} | {9, 4, 2} | {9, 4, 1} | {9, 4, 0} | {9, 3, 2} | {9, 3, 1} | {9, 3, 0} | {9, 2, 1} | {9, 2, 0} | {9, 1, 0} | {8, 7, 6} | {8, 7, 5} | {8, 7, 4} | {8, 7, 3} | {8, 7, 2} | {8, 7, 1} | {8, 7, 0} | {8, 6, 5} | {8, 6, 4} | {8, 6, 3} | {8, 6, 2} | {8, 6, 1} | {8, 6, 0} | {8, 5, 4} | {8, 5, 3} | {8, 5, 2} | {8, 5, 1} | {8, 5, 0} | {8, 4, 3} | {8, 4, 2} | {8, 4, 1} | {8, 4, 0} | {8, 3, 2} | {8, 3, 1} | {8, 3, 0} | {8, 2, 1} | {8, 2, 0} | {8, 1, 0} | {7, 6, 5} | {7, 6, 4} | {7, 6, 3} | {7, 6, 2} | {7, 6, 1} | {7, 6, 0} | {7, 5, 4} | {7, 5, 3} | {7, 5, 2} | {7, 5, 1} | {7, 5, 0} | {7, 4, 3} | {7, 4, 2} | {7, 4, 1} | {7, 4, 0} | {7, 3, 2} | {7, 3, 1} | {7, 3, 0} | {7, 2, 1} | {7, 2, 0} | {7, 1, 0} | {6, 5, 4} | {6, 5, 3} | {6, 5, 2} | {6, 5, 1} | {6, 5, 0} | {6, 4, 3} | {6, 4, 2} | {6, 4, 1} | {6, 4, 0} | {6, 3, 2} | {6, 3, 1} | {6, 3, 0} | {6, 2, 1} | {6, 2, 0} | {6, 1, 0} | {5, 4, 3} | {5, 4, 2} | {5, 4, 1} | {5, 4, 0} | {5, 3, 2} | {5, 3, 1} | {5, 3, 0} | {5, 2, 1} | {5, 2, 0} | {5, 1, 0} | {4, 3, 2} | {4, 3, 1} | {4, 3, 0} l {4, 2, 1} | {4, 2, 0} | {4, 1, 0} | {3, 2, 1} | {3, 2, 0} | {3, 1, 0} | {2, 1, 0} {120 Numbers}

Mar 12, 2018
#5
+1211
+1

Thank you! You are correct!

Lightning  Mar 13, 2018