if nine integers are chosen from between 1 and 12 inclusive, must at least one of them be odd? why? ---select--- . only of the numbers from 1 to 12 are even, so at most this many even numbers can be chosen from between 1 and 12 inclusive. hence, if nine numbers are chosen, ---select--- that at least one of them must be odd.

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12-12-2022
Mathematics

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if nine integers are chosen from between 1 and 12 inclusive, must at least one of them be odd? why? ---select--- . only of the numbers from 1 to 12 are even, so at most this many even numbers can be chosen from between 1 and 12 inclusive. hence, if nine numbers are chosen, ---select--- that at least one of them must be odd.

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contexto1019 contexto1019 · Answer 1 · 2022-12-22T20:20:03-05:00

If nine integers are chosen from between 1 and 12 inclusive, at least one of them must be odd .

if nine integers are chosen from between 1 and 12 inclusive, at least one of them must be odd. This is because there are an equal number of odd and even integers between 1 and 12 inclusive, and since 9 is an odd number, it is not possible to choose an even number of integers from this range without including at least one odd integer. To see this more formally, we can consider the possible combinations of odd and even integers that can be chosen. If we let O represent an odd integer and E represent an even integer, then the possible combinations of nine integers that can be chosen from the range 1 to 12 inclusive are: OOOEOEEEO, OOOEOEEOE, OOOEOEOEE, OOOEEOEEO, OOOEEOEOE, OOOEEOOEE, OOOEEEOEO, OOOEEEOOE, OOOEEOOEE, OOEOEEEOE, OOEOEEOEE, OOEOEOEEO, OOEOEOOE, OOEEEOEOE, OOEEEOOE, OOEEOOE, OEEOEEEO, OEEOEEOE, OEEOEOEE, OEEEOEOE, OEEEOOE, and OEEOOE. In each of these combinations, at least one of the integers chosen is odd. Therefore, if nine integers are chosen from between 1 and 12 inclusive, at least one of them must be odd.

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