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Can someone please post the approach to solve this question ?
Can someone please post the approach to solve this question ?
Q : For how many natural numbers less than 10^5 is the sum of their digits equal to 10 ?
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Answer
Hi Ryuzaki Lawliet,
Natural numbers less than 10^5 means it includes 2 digit numbers, 3 digit numbers, 4 digit numbers and maximum 5 digit numbers. Therefore, we take 5 variables
x + y + z + a + b = 10
x, y, z, a, and b can be 0 as well.
Number of ways = 10+5-1_C_5-1 = 14C4
As x, y, z, a and b are single digit numbers, they cannot take the value 10. Therefore, we need to subtract the cases where the values of x,y,x,a,b is 10. Number of such cases = 5
Number of natural numbers less than 10^5 is the sum of their digits equal to 10 = 14_C_4 - 5 = 1001 - 5 = 996
Hope this helps!
Natural numbers less than 10^5 means it includes 2 digit numbers, 3 digit numbers, 4 digit numbers and maximum 5 digit numbers. Therefore, we take 5 variables
x + y + z + a + b = 10
x, y, z, a, and b can be 0 as well.
Number of ways = 10+5-1_C_5-1 = 14C4
As x, y, z, a and b are single digit numbers, they cannot take the value 10. Therefore, we need to subtract the cases where the values of x,y,x,a,b is 10. Number of such cases = 5
Number of natural numbers less than 10^5 is the sum of their digits equal to 10 = 14_C_4 - 5 = 1001 - 5 = 996
Hope this helps!
Answer
Hey Ashish, I did see the solution in brainly yesterday but I didn't understand what x0, x1, ..., x10 represent and why is r=5. Also why are we using the splitting method in probability for this question (i.e.) why specifically this approach here ?
Answer
Search your question in google in brainly , simple solution is mentioned, if u have doubt let me know.
Smart cracku guys are not allowing to paste answer here
