SOLUTION: Howland Middle School assigns a four-digit identification number to each student. The number is made from the digits 1,2,3 and 4, and no digit was repeated. If assigned randomly

Algebra ->  Permutations -> SOLUTION: Howland Middle School assigns a four-digit identification number to each student. The number is made from the digits 1,2,3 and 4, and no digit was repeated. If assigned randomly      Log On


   

Question 1074587: Howland Middle School assigns a four-digit identification number
to each student. The number is made from the digits 1,2,3 and 4,
and no digit was repeated. If assigned randomly, what is the
probability that an ID number will end in 3?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
We find the number of SUCCESSFUL ways, those which end in 3.
That will be the numerator of the probability:

Choose the most restrictive thing first.
That's the last or 4th digit 3.

Choose the 4th digit 1 way, as 3.
Choose the 1st digit any of the remaining 3 ways, as 1, 2 o 4.
Choose the 2nd digit either of the 2 remaining ways.
Choose the 3rd digit as the 1 remaining way.

Number of SUCCESSFUL identification numbers = 3×3×2×1 = 18

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We find the number of POSSIBLE ways, those with no restrictions
That will be the denominator of the probability:

Choose the 1st digit any of the 4 ways.
Choose the 2nd digit any of the 3 remaining ways.
Choose the 3rd digit as either of the 2 remaining ways.
Choose the 4th digit as the 1 remaining way.

Number of POSSIBLE identification numbers = 4×3×2×1 = 24

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The probability is 18 SUCCESSFUL ways out of 23 POSSIBLE ways.
"OUT OF" means "OVER" or "DIVIDED BY".

Probability of a SUCCESS = 18/24 which reduces to 3/4.

Edwin