what is the sum of four digit even numbers
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the sum of 4 digit even no.iS also even...
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the sum of 4 digit even no.iS also even...
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We will have an even number when the units digit is either 0, 2 or 4
Also, 1,000th1,000th can be only 1, 2, 3 or 4 (NOT 0) as we want a 4 digit number
Case 1: Unit digit is 0
1,000th1,000th digit has 4 choices (1, 2, 3, 4) and sum of these digits =10=10
100th100th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
10th10th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
Unit digit has 1 choices (0) and sum of these digits =0=0
Now, each of the 1,000th1,000th digit will feature in 25 numbers
Similarly, each of 100th100th and 10th10thdigit will feature in 20 numbers
Also, each of the Unit digit will feature in 100 numbers
Hence, Sum of these numbers =10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+0⋅100⋅1=250,000+20,000+2,000+0=272,000=10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+0⋅100⋅1=250,000+20,000+2,000+0=272,000
Case 2: Unit digit is 2
1,000th1,000th digit has 4 choices (1, 2, 3, 4) and sum of these digits =10=10
100th100th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
10th10th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
Unit digit has 1 choices (2) and sum of these digits =2=2
Now, each of the 1,000th1,000th digit will feature in 25 numbers
Similarly, each of 100th100th and 10th10thdigit will feature in 20 numbers
Also, each of the Unit digit will feature in 100 numbers
Hence, Sum of these numbers =10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+2⋅100⋅1=250,000+20,000+2,000+200=272,200=10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+2⋅100⋅1=250,000+20,000+2,000+200=272,200
Case 3: Unit digit is 4
1,000th1,000th digit has 4 choices (1, 2, 3, 4) and sum of these digits =10=10
100th100th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
10th10th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
Unit digit has 1 choices (4) and sum of these digits =4=4
Now, each of the 1,000th1,000th digit will feature in 25 numbers
Similarly, each of 100th100th and 10th10thdigit will feature in 20 numbers
Also, each of the Unit digit will feature in 100 numbers
Hence, Sum of these numbers =10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+4⋅100⋅1=250,000+20,000+2,000+400=272,400=10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+4⋅100⋅1=250,000+20,000+2,000+400=272,400
Total Sum of All Numbers =250,000+272,200+272,400=794,600=250,000+272,200+272,400=794,600
Hope this helps u Please make me as a brainliest
Also, 1,000th1,000th can be only 1, 2, 3 or 4 (NOT 0) as we want a 4 digit number
Case 1: Unit digit is 0
1,000th1,000th digit has 4 choices (1, 2, 3, 4) and sum of these digits =10=10
100th100th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
10th10th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
Unit digit has 1 choices (0) and sum of these digits =0=0
Now, each of the 1,000th1,000th digit will feature in 25 numbers
Similarly, each of 100th100th and 10th10thdigit will feature in 20 numbers
Also, each of the Unit digit will feature in 100 numbers
Hence, Sum of these numbers =10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+0⋅100⋅1=250,000+20,000+2,000+0=272,000=10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+0⋅100⋅1=250,000+20,000+2,000+0=272,000
Case 2: Unit digit is 2
1,000th1,000th digit has 4 choices (1, 2, 3, 4) and sum of these digits =10=10
100th100th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
10th10th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
Unit digit has 1 choices (2) and sum of these digits =2=2
Now, each of the 1,000th1,000th digit will feature in 25 numbers
Similarly, each of 100th100th and 10th10thdigit will feature in 20 numbers
Also, each of the Unit digit will feature in 100 numbers
Hence, Sum of these numbers =10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+2⋅100⋅1=250,000+20,000+2,000+200=272,200=10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+2⋅100⋅1=250,000+20,000+2,000+200=272,200
Case 3: Unit digit is 4
1,000th1,000th digit has 4 choices (1, 2, 3, 4) and sum of these digits =10=10
100th100th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
10th10th digit has 5 choices (0, 1, 2, 3, 4) and sum of these digits =10=10
Unit digit has 1 choices (4) and sum of these digits =4=4
Now, each of the 1,000th1,000th digit will feature in 25 numbers
Similarly, each of 100th100th and 10th10thdigit will feature in 20 numbers
Also, each of the Unit digit will feature in 100 numbers
Hence, Sum of these numbers =10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+4⋅100⋅1=250,000+20,000+2,000+400=272,400=10⋅25⋅1000+10⋅20⋅100+10⋅20⋅10+4⋅100⋅1=250,000+20,000+2,000+400=272,400
Total Sum of All Numbers =250,000+272,200+272,400=794,600=250,000+272,200+272,400=794,600
Hope this helps u Please make me as a brainliest
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