Question

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?

Answer 1

1/2

Answer 2

no, 1/5

Answer 3

Good, show me how?

Answer 4

it can start with a zero, and the answer is 1/5

Answer 5

Nevermind then.

Answer 6

lol

Answer 7

1/5

Answer 8

over 6 billion or greater than or equal to 6 billion?

Answer 9

It cannot be = to 6 billion

Answer 10

Zark it doesn't matter since each digit is used once. No way it can be exactly 6 billion.

Answer 11

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

Answer 12

ok

Answer 13

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

Answer 14

then 1/5

Answer 15

\[\frac{2\cdot 5\cdot 8!+2\cdot 4\cdot 8!}{10!}\]

Answer 16

man i wish satellite was here, zarkon can you explain that

Answer 17

didn't you get that....????

Answer 18

yes but you're way is long, satellite can do these like zarkon did there which is useful for me on quick, timed tests

Answer 19

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!

Answer 20

if we use 7 or 9 for the first digit we have 5 choices for the ones digit...

Answer 21

why do you use 8!?

Answer 22

8! ways to arrange 8 numbers in a row

Answer 23

okay