<p>Hi there.</p>
<p>Can someone please explain the approach for this question:</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>Why is 4 x 4 x 3 / 3 x 2 x 1 NOT correct?</p>
<p>The right answer is 24. I mean obviously they did it this way: 4 x (4 x 3 : 2)
But why? Thanks.</p>
<p>I don’t know if this is incorrect logic but…</p>
<p>4 experienced workers
4 trainees
3 make a team</p>
<p>1 trainee 1 experienced
--------- = -------------
1 experienced 2 trainees</p>
<p>3 x 4 experienced ones x 4 trainees x 1 experienced one
-----------------
2 trainees</p>
<p>3 x 4 experienced x 2 trainees x 1 experienced = 24</p>
<p>It’s a “combination” problem:</p>
<p>3 * (4 nCr 2)</p>
<p>^^(the nCr function is in the “MATH” section of a TI-93/94 calc, under “Probability,” and is pronounced ___ pick ___, in this case, it’s 4 pick 2. If you use this function, or use an online combination calculator here: [Combinations</a> Calculator (nCr)](<a href=“Combinations Calculator (nCr)”>Combinations Calculator (nCr)), 4 nCr 2 = 6), so:</p>
<p>3 * (4) = 24</p>