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Find sum of all the number greater than 10000 formed by the digits 0,2,4,6,8 no digit being repeted?

Find sum of all the number greater than 10000 formed by the digits 0,2,4,6,8 no digit being repeted?

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Raj
 

1. Fix the units digit of the 5 digit number . say _ _ _ _ 2 
2. The total of such numbers with 2 in the units place is 4! i,e 24 
3. In the same manner there are 24 such numbers that end with 0,4,6 & 8 
4. Now the sum of all the numbers in the Units place is 
24 * (0+2+4+6+8) = 24 * 20 = 480 
5. The same is true for the 10th place, 100th place, 1000th place & 10,000th place. 
Hence the sum of all the 5 digit numbers using 0,2,4,6,8 is 
480 (1+10+100+1000+10000) 
= 480 (11111) 
= 5333280-----------------------------(A) 
6. Following the same approach as mentioned in steps 1 to 5, 
the sum of all the 4 digit numbers (5 digit numbers starting with 0 ) 
is 
= 6*(2+4+6+8)* (1+10+100+1000) 
= 6* 20 * 1111 
= 133320--------------------------------(B) 

7. Hence the sum of all the 5 digit numbers using 0,2,4,6,8 > 10000 
= (A) - (B) 
= 5333280 - 133320 

= 5199960 
 
Regards
Arun(askIITians forum expert)

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