IIT JEE , AIEEE Forum - Mathematics , Algebra

rik_mad

look, trying to find the sum to be multiple of 9 for 9c7 numbers (which is 36) is absolutely impractical.
u cud try this,
the smallest possible sum of seven numbers will be
1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
and the largest possible sum is
3 + 4 + 5 + 6 + 7 + 8 + 9 = 42.
there is only one number between 28 and 42 which is divisible by 9 which is 36
36 hmmmm..which means 4 times 9
wat r the combinations of numbers which can give u nine
clearly they are
1 + 8
2 + 7
3+ 6
4 + 5
and 9 itself
in all there are 5 such elements possible
now u can't choose the first four elements as then ur total number of elements will be 8
so only 4c3(the frst four)= 4 combinations r possible which along with digit 9 will give 36.
now ur probabilty will become
7! * (4) / (9c7 * 7!)
where i hav used 7! for finding different permutations within the selected numbers
so probabilty is 4/36 = 1/9
simple !!

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