Will someone plz explain to me, or refer me to a Sal video that explains how i would be able to solve the following question.
Set X= { 6, -8, 9, 11, -14, 15}
Set Y= { 2, 7, -12, 16, -19, -20}
Set Z= { -4, 5, -10, -13, 17, -22 }
If one number is chosen from each set to form a group, how many groups of numbers can be made such that their product is negative?
I'm pretty sure there are no videos about these kind of questions, but here's my answer:
If you're trying to figure out if the product of three numbers is positive or negative the only thing that matters is if the number is positive or negative. So the numbers 6, 9 and 11 can be treated in a similar way. So let's figure out how many positive and negative values are in each set.
Set X: 4 positive, 2 negative
Set Y: 3 positive, 3 negative
Set Z: 2 positive, 4 negative.
To get a negative number we need to multiply a negative number with two positive numbers or multiply three negative numbers.
Let's start with multiplying three negative numbers. Set X has 2 negative numbers, set Y 3 and set Z 4. So there are 2 * 3 * 4 = 24 ways to multiply three negative numbers.
Now the harder one where only one number is negative.
There are 2 negative numbers in set X, 3 positive numbers in Y and 2 positive numbers in Z. So there are 2 * 3 * 2 = 12 ways to multiply two positive numbers and one negative number if the negative number comes from set X.
So what if the negative number comes from set Y? That makes 4 positive numbers from X * 3 negative numbers from Y * 2 positive numbers from Z = 24.
Last but not least, what if the negative number comes from set Z? 4 * 3 * 4 = 48.
Add all those options together (24 + 12 + 24+ 48) = 108 ways.
I hope that helped you.
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