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Let-S-1-2-3-4-28-29-30-How-many-subgroups-of-3-elements-are-in-the-S-so-that-their-sum-is-a-multiple-of-3-The-answer-is-1-360-subgroups-




Question Number 178213 by Acem last updated on 14/Oct/22
Let S= {1, 2, 3, 4, ..., 28, 29, 30}   How many subgroups of 3 elements are in the S    so that their sum is a multiple of 3     The answer is 1 360 subgroups
LetS={1,2,3,4,,28,29,30}Howmanysubgroupsof3elementsareintheSsothattheirsumisamultipleof3Theansweris1360subgroups
Commented by Acem last updated on 14/Oct/22
Hint: n mod 3 = {0, 1, 2} ∀n∈ N
Hint:nmod3={0,1,2}nN
Answered by nikif99 last updated on 14/Oct/22
Let S_0 ={3, 6, 9, ..., 30} n=10  S_1 ={1, 4, 7, ..., 28} n=10  S_2 ={2, 5, 8, ..., 29} n=10  Sum divisible by 3:  a) 1 element from each S_0 , S_1 , S_2 : 10^3   b) 3 elements from S_0 : C_3 ^(10) =120  c) 3 elements from S_1 : C_3 ^(10) =120  d) 3 elements from S_2 : C_3 ^(10) =120  Total 1360
LetS0={3,6,9,,30}n=10S1={1,4,7,,28}n=10S2={2,5,8,,29}n=10Sumdivisibleby3:a)1elementfromeachS0,S1,S2:103b)3elementsfromS0:C310=120c)3elementsfromS1:C310=120d)3elementsfromS2:C310=120Total1360
Commented by Acem last updated on 14/Oct/22
A bouquet of flowers!
Abouquetofflowers!
Commented by nikif99 last updated on 14/Oct/22
Thank you.
Thankyou.
Commented by Tawa11 last updated on 15/Oct/22
Great sir
Greatsir

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