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In how many ways 3 digit number like XYZ can be formed where Z>Y>X ?

In how many ways 3 digit number like XYZ can be formed where Z>Y>X ?

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
x=1
y=2 z= 3...9 (7 ways)
y=3 z= 4...9 (6 ways)
...
y=8 z= 9 (1 way)

Total : 7+6+...+1
x=2
y=3 z= 4...9 (6 ways)
y=4 z= 5...9 (5 ways)
...
y=8 z= 9 (1 way)
Total : 6+5+...+1
...
x=6
y=7 z= 8,9 (2 ways)
y=8, z=1 (1 way)
Total : 2+1
x =7
y = 8 z = 9(1 way)

Total : 1

Required number of ways = ( 7+6+...+1) + (6+5+...+1) + (5+4+3+2+1) + (4+3+2+1) + (3+2+1) + (2+1) + 1
=28+21+15+10+6+3+1
= 84

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