Question 231590: The digits 1, 2, 3, 4, and 5 are randomly arranged to form a five-digit number. Find the probability of each of the following events.
(a) the number is even.
(b) the first and last digits of the number both are even
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The digits 1, 2, 3, 4, and 5 are randomly arranged to form a five-digit number. Find the probability of each of the following events.
(a) the number is even.
It will be even if the last digit is even.
# of ways to pick the last digit: 2
# of ways to arrange the remaining 4 digits: 4!
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Total # of 5-digit numbers with the restriction: 2*4! = 2*48
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(b) the first and last digits of the number both are even
# of ways to pick the 1st digit: 2
# of ways to pick the last digit: 1
# of ways to arrange the remaining 3 digits: 3! = 6
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Total # of 4-digit numbers with the restriction: 2*1*6 = 12
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Cheers,
Stan H.
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