Math, asked by srivarsha9778, 1 year ago

How many integer numbers between 0 and 9999 are there that have exactly one digit 1 and exactly one digit 3?

Answers

Answered by amitnrw
1

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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