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Question Number 41754 by Tawa1 last updated on 12/Aug/18

Answered by candre last updated on 12/Aug/18

we have from 1 to 1000 number that can have 3  3××  ×3×  ××3  separating cases  ××3:  10×10=100(9×9=81)  ×3×:  10×10=100(9×9=81)  3××:  10×10=100(9×9=81)  analysying the intersection  ×33:10(9)  3×3:10(9)  33×:10(9)  333:1  so, by inclusion exclusion principe  100+100+100−10−10−10+1=271  or, counting alredy excluding overlaping (() one)  81×3+9×3+1=271

wehavefrom1to1000numberthatcanhave33×××3×××3separatingcases××3:10×10=100(9×9=81)×3×:10×10=100(9×9=81)3××:10×10=100(9×9=81)analysyingtheintersection×33:10(9)3×3:10(9)33×:10(9)333:1so,byinclusionexclusionprincipe100+100+100101010+1=271or,countingalredyexcludingoverlaping(()one)81×3+9×3+1=271

Commented by Tawa1 last updated on 12/Aug/18

God bless you sir

Godblessyousir

Answered by tanmay.chaudhury50@gmail.com last updated on 12/Aug/18

  1)single digit number using 3 is =1  2)two digit number unit place is 3 then tength   place can be filled by using (1,2,3,4,5,6,7,8,9)  9 ways so =9  3)two digit number tength place is 3 then unit  place can be (0 ,1,2,3,4,5,6,7,8,9)=10    4)three digit  number hundred place is 3  tenth place (0, 1, 2 ,3, 4, 5, 6, 7, 8, 9) 10was  similarly unit place 10ways=1×10×10=100  5)three digit number tength place is 3  hundred place(1 ,2 ,3 ,4, 5 ,6 ,7 ,8 ,9)=9ways  unit place (0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9)=10 ways  1×9×10=90  6)three digit number unit place is 3  tength place (0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9)  hundred place(1, 2^�  3, ^� 4 ,5 ,6 ,7 ,8 ,9)  1×10×9=90  so total =1+9+10+100+90+90=300

1)singledigitnumberusing3is=12)twodigitnumberunitplaceis3thentengthplacecanbefilledbyusing(1,2,3,4,5,6,7,8,9)9waysso=93)twodigitnumbertengthplaceis3thenunitplacecanbe(0,1,2,3,4,5,6,7,8,9)=104)threedigitnumberhundredplaceis3tenthplace(0,1,2,3,4,5,6,7,8,9)10wassimilarlyunitplace10ways=1×10×10=1005)threedigitnumbertengthplaceis3hundredplace(1,2,3,4,5,6,7,8,9)=9waysunitplace(0,1,2,3,4,5,6,7,8,9)=10ways1×9×10=906)threedigitnumberunitplaceis3tengthplace(0,1,2,3,4,5,6,7,8,9)hundredplace(1,2¯3,¯4,5,6,7,8,9)1×10×9=90sototal=1+9+10+100+90+90=300

Commented by Tawa1 last updated on 12/Aug/18

God bless you sir

Godblessyousir

Answered by MrW3 last updated on 12/Aug/18

3: ⇒1    3X: ⇒9  X3: ⇒8  33: ⇒1×2=2  Σ=19    3XY: ⇒9×9=81  X3Y: ⇒8×9=72  XY3: ⇒8×9=72  33X: ⇒2×9=18  3X3: ⇒2×9=18  X33: ⇒2×8=16  333: ⇒1×3=3  Σ=280    ⇒1+19+280=300

3:13X:9X3:833:1×2=2Σ=193XY:9×9=81X3Y:8×9=72XY3:8×9=7233X:2×9=183X3:2×9=18X33:2×8=16333:1×3=3Σ=2801+19+280=300

Commented by Tawa1 last updated on 12/Aug/18

God bless you sir

Godblessyousir

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