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Question 4 How many integer numbers between 0 and 9999 are there that have exactly one digit 1 and exactly one digit 3

Sagot :

MrRoyalidn

Answer:

768 numbers

Step-by-step explanation:

Given

[tex]Digits = \{0,1,2,3,4,5,6,7,8,9\}[/tex]

Required

Number of digits between 0 ad 9999 that have one 1 and one 3

There are a total of 4 digits that make up any of the numbers in 0 to 9999 with the given condition

This can be represented as WXYZ

  • Digit 1 can occupy any of the 4 positions
  • Digit 3 can occupy any of the 4 - 1 positions

The remaining 8 digits will occupy the last 2 positions in the following ways:

  • The first of the 8 digits can be selected from any of [tex]\{0,2,4,5,6,7,8,9\}[/tex] i.e. 8 ways
  • The second can be selected from any of [tex]\{0,2,4,5,6,7,8,9\}[/tex] i.e. 8 ways

So, the total number of selection is:

[tex]Total = 4 * (4 - 1) * 8 * 8[/tex]

[tex]Total = 4 * 3 * 8 * 8[/tex]

[tex]Total = 768[/tex]

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