Question 471498: form a four-digit numbers using the set of digits {0, 1, 2, 3, 4, 5, 6}. If one four-digit number is chosen at random from all those that can be made, find the probability that the one chosen does not end with a 3.
Answer by Edwin McCravy(20055)   (Show Source):
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form a four-digit numbers using the set of digits {0, 1, 2, 3, 4, 5, 6}. If one four-digit number is chosen at random from all those that can be made, find the probability that the one chosen does not end with a 3.
First we calculate the numerator of the probability:
We can choose the digits in any order. So we choose the most restrictive digit first.
We can choose the fourth digit any of 6 ways 0,1,2,4,5,or 6, just not 3.
We can choose the first digit any of 6 ways (because we can choose the 3 for the first digit)
We can choose the second digit any of 5 ways
We can choose the third digit any of 4 ways.
So the numerator of the probability is 6*6*5*4
Next we calculate the denominator of the probability:
There is no restriction here, so we'll just choose them left to right
We can choose the first digit any of 7 ways
We can choose the second digit any of 6 ways
We can choose the third digit any of 5 ways.
We can choose the fourth digit any of 4 ways
So the denominator of the probability is 7*6*5*4
The probability is then 
Edwin
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