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Question Number 34718 by tawa tawa last updated on 10/May/18

How many numbers greater than 350 can be formed from 1, 2, 3, 4 and 5

$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{350}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\:\mathrm{and}\:\mathrm{5} \\ $$

Answered by Rasheed.Sindhi last updated on 10/May/18

1dd<350 2dd<350 3dd:355 (One number) (Each of Tens & units digit can be filled in only one way. 1×1×1=1) 4dd & 5dd: 2×5×5=50 numbers Hundreds in 2 ways Tens in 5 ways. Ones in 5 ays Hence 1+50=51 numbers

$$\mathrm{1dd}<\mathrm{350} \\ $$$$\mathrm{2dd}<\mathrm{350} \\ $$$$\mathrm{3dd}:\mathrm{355}\:\left(\mathrm{One}\:\mathrm{number}\right) \\ $$$$\:\:\left(\mathrm{Each}\:\mathrm{of}\:\mathrm{Tens}\:\&\:\mathrm{units}\:\mathrm{digit}\:\mathrm{can}\:\mathrm{be}\:\mathrm{filled}\right. \\ $$$$\left.\:\:\:\:\:\:\:\mathrm{in}\:\mathrm{only}\:\mathrm{one}\:\mathrm{way}.\:\mathrm{1}×\mathrm{1}×\mathrm{1}=\mathrm{1}\right) \\ $$$$\mathrm{4dd}\:\&\:\mathrm{5dd}:\:\mathrm{2}×\mathrm{5}×\mathrm{5}=\mathrm{50}\:\mathrm{numbers} \\ $$$$\:\:\:\:\:\:\:\mathrm{Hundreds}\:\:\mathrm{in}\:\mathrm{2}\:\mathrm{ways} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Tens}\:\mathrm{in}\:\mathrm{5}\:\mathrm{ways}. \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{Ones}\:\mathrm{in}\:\mathrm{5}\:\mathrm{ays} \\ $$$$\mathrm{Hence}\:\mathrm{1}+\mathrm{50}=\mathrm{51}\:\mathrm{numbers} \\ $$

Commented by Joel579 last updated on 10/May/18

4 digits = 5^4 = 625 5 digits = 5^5 = 3125 Total = 51 + 625 + 3125 = 3801

$$\mathrm{4}\:\mathrm{digits}\:=\:\mathrm{5}^{\mathrm{4}} \:=\:\mathrm{625} \\ $$$$\mathrm{5}\:\mathrm{digits}\:=\:\mathrm{5}^{\mathrm{5}} \:=\:\mathrm{3125} \\ $$$$\mathrm{Total}\:=\:\mathrm{51}\:+\:\mathrm{625}\:+\:\mathrm{3125}\:=\:\mathrm{3801} \\ $$

Commented by Joel579 last updated on 11/May/18

Since the question didn′t tell us how many digits they want, I think 4 and 5 digits number can also be included

$$\mathrm{Since}\:\mathrm{the}\:\mathrm{question}\:\mathrm{didn}'\mathrm{t}\:\mathrm{tell}\:\mathrm{us}\:\mathrm{how}\:\mathrm{many} \\ $$$$\mathrm{digits}\:\mathrm{they}\:\mathrm{want},\:\mathrm{I}\:\mathrm{think}\:\mathrm{4}\:\mathrm{and}\:\mathrm{5}\:\mathrm{digits}\:\mathrm{number} \\ $$$$\mathrm{can}\:\mathrm{also}\:\mathrm{be}\:\mathrm{included} \\ $$

Commented by tawa tawa last updated on 05/Jun/18

what of : 351, 352, 353, 354, 355 = 5 numbers not 1

$$\mathrm{what}\:\mathrm{of}\::\:\:\:\mathrm{351},\:\mathrm{352},\:\mathrm{353},\:\mathrm{354},\:\mathrm{355}\:\:=\:\:\mathrm{5}\:\mathrm{numbers}\:\mathrm{not}\:\mathrm{1} \\ $$

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