even numbers

Probability Level 3

How many four digit EVEN numbers have all 4 digits distinct?


The answer is 2296.

Hemlata Sharma by Hemlata Sharma , 27, India

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2 solutions

Hemlata Sharma
Jun 2, 2014

9 . 8 . 7 . 5 - 8 . 7 . 4 = 2520 - 224 = 2296 digits

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No, It's 8 8 7*5 because, you can never use 0 as a first digit

Tierone James Santos - 6 years, 11 months ago
Fox To-ong
Feb 17, 2015

First,consider the case of 0 as last digit. There are 10 numbers in total from 0 to 9. Then,the total no. of numbers having 0 as the last digit is 9 X 8 X 7=504

Now consider the case of 2 as last digit. The total no. of numbers having 2 as the last digit is also 9 X 8 X 7=504

But,it will include numbers having 0 as first digit.eg:0932 So,we have to remove such numbers from this list. Total no. of Numbers with 0 as first digit and 2 as last digit = 8 X 7=56 (since 2 numbers are already fixed)

So,subtracting 56 from 504 gives 448 This is same for numbers with 4,6 and 8 as last digits. So,total number of legal numbers with 2,4,6,8 as last digits= 448 X 4=1792

Adding total no. of numbers having 0 as last digit to this 1792,we get 1792+504 = 2296 final answer

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