How many integer numbers between 0 and 9999 are there that have exactly one digit 1 and exactly one digit 3?
Answers
Given : numbers between 0 and 9999 are there that have exactly one digit 1 and exactly one digit 3
To Find : How many numbers
Solution:
Two digit numbers , 13 & 31
Three Digit numbers :
13X , 31X , 1X3 , 13X , X13 , X31
X can have 8 Digits.
4 * 8 + 7 * 2 or
1st digit 1 or 3 + 1st Digit not 1 or 3
²C₁*⁸C₁*2! + ⁷C₁* ²C₂*2!
= 46
Four Digit numbers
1st Digit 1 or 3 + 1st Digit not 1 or 3
²C₁*⁸C₁*⁸C₁*3!/2 + ⁷C₁*⁸C₁*3!
= 384 + 336
= 720
2 + 46 + 720
=768
768 numbers from 0 to 9999 have exactly one digit 1 and exactly one digit 3
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