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Permutations and Rule of Sum question?
How many five-digit even numbers can be formed using all the digits 0, 1, 2, 3, and 4? Thanks in advance
1 Answer
- husoskiLv 72 months agoFavorite Answer
The final digit must be 0, 2 or 4 for an even number. There are 3 choices for that, times 4! = 24 ways to arrange the remaining 4 digits. 3*24 = 72 in all. That's how many arrangements of those 5 digits end with an even digit.
But a "five-digit number" can't begin with 0, so eliminate the arrangements beginning with 0. Among those, the final digit is a 2 or 4 so there are 2 choices for that times 3!=6 ways to arrange the remaining 2 digits. 2*6 = 12 arrangements begin with 0 and end with 2 or 4.
Subtract 72 - 12 to get 60 different 5-digit even numbers.
