<p>If x+y=7 and xy=4, then find the value of x^2+y^2.</p>
<p>This sinewy and byzantine problem has left me baffled, perplexed and utterly confused. Please solve this intimidating peace of drudgery!</p>
<p>Haha^ Some great vocab practice with it too!</p>
<p>(x+y) ^2 = x^2 + 2xy + y^2
49 = x^2 + 2(4) + y^2
41 = x^2 + y^2</p>
<p>Thanks Catmeow, Really Helpful and Concise.</p>
<p>Can someone answer this one?</p>
<p>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>I keep getting 48, when I do 4x4x3. But I know now that I am to do combination. Can I do this in my calculator using the nCR key? If so, how would this work?</p>
<p>BUMP 10char</p>
<p>I would just list out all the combinations for this problem. There are six different pairs of trainees that can go with each experienced plumber, so 6x4=24 teams are possible.</p>
<p>you only have to use combinations for the trainees part. There’s 4 trainees, and you need to choose 2. So do 4 nCr 2. You get 6, and multiply that by the experienced plumbers.</p>
<p>Doing 4x4x4, I get 48, If I divide this by 2, i get the right answer. Is this a good method?</p>
<p>^^^^^^^^^^^ NONONONONONONO that is a terrible method. It has no logic behind it, and most likely will not work for every question. Just understand the method using combinations (or you can even just draw the question out! if you wanna waste the time)</p>
<p>You have 4 leaders in which you choose one for the team. So you have 4 combinations.
Then you must find the amount of combinations for the trainees on the team. You can choose two out of the four (and you don’t want repeats, like choosing person 1 and person 2, then choosing person 2 and person 1 for another team), so it must be combinations. So do 4 nCr 2, and you get 6 different combinations of trainee plumbers. Therefore, you multiple 4 by 6 and get 24 total combinations.</p>
<p>I agree with satman. Just think of it this way: You have 4 ways to pick the first trainee, 3 ways to pick the second. You have to divide by 2! to deal with overcounting, so there are 4*3/2! = 6 ways to pick the trainees. Now we multiply by 4 (more precisely: 4C1) to account for experienced plumbers. 6x4 = 24.</p>
<p>No calculator needed!</p>