Question 1138214: Five cards numbered with the digits 3,4,5,6,7,8 are shuffled and laid in a row to make a five-digit number. What is the probability that this number is divisible by 9?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
This could have been an interesting problem if you had stated it correctly....
With one digit on each card, 6 different digits and only 5 cards is inconsistent.
Re-post your problem; and pay attention to what you have written when you submit your post.
Answer by ikleyn(52810)  (Show Source):
You can put this solution on YOUR website! .
 Six cards numbered with the digits 3,4,5,6,7,8 are shuffled and laid in a row to make a five-digit number.
What is the probability that this number is divisible by 9?
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3 + 4 + 5 + 6 + 7 + 8 = 33.
a) 33 - 3 = 30
b) 33 - 4 = 29
c) 33 - 5 = 28
d) 33 - 6 = 27
e) 33 - 7 = 26
f) 33 - 8 = 25.
So, we have 6 cases (6 sums), and we see that among the sums of any 5 cards, only one is divisible by 9 :
it is case d), where the sum is 27.
Therefore, the probability under the question is  .
Solved and answered.
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