<p>This is from test 5.
Again, a combinations problem. I suck at these. Haha.</p>
<p>Section 3, number 15:
"The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible?"</p>
<p>The answer is 24.
I know how to get to the answer. But I don't understand the why. I never have, and I still don't. Heh.
It's just 4 (only 1 spot for experienced plumber) * 4 nCr 2 (plug in calculator).
Why?
Why 4 nCr 2 and not 4 nPr 2? I always forget the difference between the two. Gah. Someone please help :)</p>
<p>And another question:
Section 9, number 11:
In the xy-coordinate plane, line m is the reflection of line l about the x-axis. If the slope of line m is -4/5, what is the slope of line l?</p>
<p>How do you do these? I've completely forgotten..</p>
<p>Use nCr when order does not matter. Use nPr when order matters.</p>
<p>In other words, when you’re picking the trainees, it doesn’t matter if you pick Tom first and Jerry second, or Jerry first and Tom second. Either way, you’ll get Tom and Jerry on the job.</p>
<p>Other question: try sketching it. (the answer is 4/5, btw - flipping across the x-axis is equivalent to multiplying by -1.)</p>
<p>A slope of -4/5 means “go down 4, right 5” to get from one point to the next. For example, if you start at (0,0) then the next point would be (5,-4). The reflection of this point in the x-axis is (5,4). So from (0,0) you go up 4, right 5. Thus, the slope is 4/5.</p>
<p>Since there are 4 experience plumbers and 1 spot, there are 4 possibilities of plumbers.</p>
<p>Since there are 2 spots for 4 trainees, and order does not matter, use combinations. (Use combinations whenever you are choosing members for a team or group because order will not matter). The combination will be 4 C 2 = 6. That just means 4 trainees for 2 spots.</p>
<p>Using the multiplication counting principle, you will do 4 x 6 = 24</p>