Given the set A=(-6,-5,-4,-3,-2,-1,1,2,3,4,5,6)
In how many ways can you select four different numbers so that their product is negative? Explain your soulution
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2Hint: One negative or three negative, the rest positive. – André Nicolas Oct 05 '15 at 02:16
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I do not understand the hint? – John Oct 05 '15 at 02:30
1 Answers
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The product of four non-zero numbers is negative precisely if one of the numbers is negative or three of the numbers are negative.
One negative: The negative number can be chosen in $\binom{6}{1}$ ways, and the three positives that keep it company can then be chosen in $\binom{6}{3}$ ways, for a total of $\binom{6}{1}\binom{6}{3}$.
Three negative: It's your turn.
Finally, add.
André Nicolas
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1The final answer will be $\binom{6}{1}\binom{6}{3}+\binom{6}{3}\binom{6}{1}$, presumably calculated out. In my answer, nowhere did it say to add $\binom{6}{1}$ and $\binom{6}{3}$. – André Nicolas Oct 05 '15 at 02:46
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1Yes, it is $240$. But the key thing is understanding the reasoning. – André Nicolas Oct 05 '15 at 02:50
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