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Taking one, two, three and four digits from digits $1,2,7$ and $8$, and if repetitions are not allowed

  1. How many different numbers can be arranged?
  2. How many of them would be greater than $200$?

I got the first answer $= 64$:

  • $4$ one digit numbers
  • $12$ two digit numbers
  • $24$ three digit numbers
  • $24$ four digit numbers

total $= 64$

How to know how many are above $200$ though?

Jimmy R.
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HN17
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  • Hint. Assuming your counts are correct so far (I haven't checked) - what fraction of the three digit numbers are greater than 200? What about the one, two and four digit numbers? – Ethan Bolker Dec 02 '16 at 13:59

1 Answers1

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Your calculations for the firs question are correct. For the second, any $4$ digit number is $>200$ and any three digit number that starts with $2,7$ or $8$. Hence, $3$ out of $4$ three digit numbers are above $200$, which gives you a total of $$24+\frac{3}{4}24=42$$ numbers above 200.

Jimmy R.
  • 35,868
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    Correct and nicely said, so upvoted. That said I'd rather you'd waited a while so the OP could try for him or herself with the hint, and maybe learn a little more. – Ethan Bolker Dec 02 '16 at 14:04
  • @EthanBolker Thanks, and ... thanks, you are right, I will keep that in mind. – Jimmy R. Dec 02 '16 at 14:08