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From these four digits '0' cannot be at first place to form four digit number

so we have 1, 2, or 3 can be at thousand's place

keeping one digit at thousand place can have 6 different four digit number

so that means

1000*6 + 2000* 6 + 3000* 6 = 36000

Now come to hundred's place we can have all four digit at this place , '0' will not contribute any thing to sum so in all four digits number 1,2,3 will be at 4 times on same place

so that means

100*4 + 200* 4 + 300 * 4= 2400

Now come to tenth's place ...same as hundred

so

10*4 + 20*4 + 30*4= 240

same for unit place

1*4 + 2*4 + 3*4= 24

in last if you add whole the total sum of all possible four digit number formed is38664

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Q: What is the sum of all the four digit numbers formed using the digits 0 1 2 and 3 None of the two digits should be repeated?
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Numbers formed should be of at least 3 digits means they may be of 3 digits, 4 digits, 5 digits or 6 digits. There are 6 choices for digit in the units place. There are 5 and 4 choices for digits in ten and hundred’s place respectively. So, total number of ways by which 3 digits numbers can be formed = 6.5.4 = 120 Similarly, the total no.of ways by which 4 digits numbers can be formed = 6.5.4.3 = 360. the total no. of ways by which 5 digits numbers can be formed = 6.5.4.3.2 = 720. The total no.of ways by which 4 digits numbers can be formed = 6.5.4.3.2.1 = 720. So, total no.of ways by which the numbers of at least 3 digits can be formed = 120 + 360 + 720 + 720 = 1920.


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Related questions

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