anonymous
  • anonymous
Tough probability question: What is the probability that a number formed using each of the digits 0-9 once is an even number over 6 billion?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Savvy
  • Savvy
1/2
Savvy
  • Savvy
no, 1/5
anonymous
  • anonymous
Good, show me how?

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More answers

anonymous
  • anonymous
it can start with a zero, and the answer is 1/5
anonymous
  • anonymous
Nevermind then.
anonymous
  • anonymous
lol
phi
  • phi
1/5
Zarkon
  • Zarkon
over 6 billion or greater than or equal to 6 billion?
phi
  • phi
It cannot be = to 6 billion
anonymous
  • anonymous
Zark it doesn't matter since each digit is used once. No way it can be exactly 6 billion.
anonymous
  • anonymous
doesnt matter really because if the first number is a 5 its going to be less and if its 6 its going to be greater
Zarkon
  • Zarkon
ok
Savvy
  • Savvy
we need to make a 10 digit no. from 0-9 without repitition... total no. of ways are 10! now we need to make cases: CASE I : no. ends with a zero so total ways of making a no. over 6 billion are like at first position only 4 nos. are allowed i.e 6,7,8,9 and last is zero, rest arranged by 8! so total such nos. are 4X8! CASE II: no.ends with 6 or 8 for last place we have 2 choices for first place we have only 3 choices since one of 6 or 8 has been consumed at the last place rest arrange as 8! so total of this case = 6X8! CASE III: no. ends with 2 or 4 last place; 2 choices first place; 4 choices rest arrange as 8! total for this case = 8X8! now total favourable cases = 8X8! + 6X8! + 4X8! = 18X8! probability = (18X8!)/10! = 1/5
Zarkon
  • Zarkon
then 1/5
Zarkon
  • Zarkon
\[\frac{2\cdot 5\cdot 8!+2\cdot 4\cdot 8!}{10!}\]
anonymous
  • anonymous
man i wish satellite was here, zarkon can you explain that
Savvy
  • Savvy
didn't you get that....????
anonymous
  • anonymous
yes but you're way is long, satellite can do these like zarkon did there which is useful for me on quick, timed tests
Zarkon
  • Zarkon
the first digit can be 6,7,8,9 look at 6 and 8 first ...since the ones digit has to be even we have only 4 choices remaining. now pick the 8 remaining numbers for the middle..thus 2*4*8!
Zarkon
  • Zarkon
if we use 7 or 9 for the first digit we have 5 choices for the ones digit...
anonymous
  • anonymous
why do you use 8!?
Zarkon
  • Zarkon
8! ways to arrange 8 numbers in a row
anonymous
  • anonymous
okay

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