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Re: If 0, 1, 2, 3, and 4 are arranged to form a four-digit number, how man [#permalink]
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Since the five numbers constitute a five-digit even number, the first digit cannot be zero. Furthermore, the last digit must be one of the three even numbers. The middle three numbers can then be arranged through a permutation from the remaining three numbers:

5 • 3 • \(3_{P}_3\) = 15 • 3! = 90.
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Re: If 0, 1, 2, 3, and 4 are arranged to form a four-digit number, how man [#permalink]
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the question is asking to form a 4-digit number. i think the answer should be 60.
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Re: If 0, 1, 2, 3, and 4 are arranged to form a four-digit number, how man [#permalink]
In the qn,it is not mentioned that number repetition is allowed or not so:
with repetition:
thousandth place can be filled in 4 ways as 0 is not possible
hundredth place can be filled in 5 ways
tenth place can be filled in 5 ways
unit place can be filled in 3 ways(0,2,4) == 4*5*5*3 ->300 ways

without repetition:
thousandth place can be filled in 4 ways as 0 is not possible
unit place can be filled in 3 ways(0,2,4)
hundredth place can be filled in 3 ways
tenth place can be filled in 2 ways
== 4*3*2*3 ->72 ways


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Re: If 0, 1, 2, 3, and 4 are arranged to form a four-digit number, how man [#permalink]
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Fixed. Thank you
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Re: If 0, 1, 2, 3, and 4 are arranged to form a four-digit number, how man [#permalink]
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