Question 169882
<font size = 7 color = "red"><b>Warning: Stanbon's
(b) and (c) are incorrect.
Edwin's solution:</b></font>

A box contains 74 brass washer, 86 steel washers and 40 aluminium washers. Three washers are drawn at random from the box without replacement. 
a) Determine the probability that all three are steel washers. 
<pre><font size = 4 color="indigo"><b>
There are 86 steel washers.
There are {{{74+86+40}}} or {{{200}}} washers.  So the
desired probability is

 86 choose 3
------------
200 choose 3

{{{86C3/200C3 = 102340/1313400 = .0779199025}}}

</pre></font></b>
b) Determine the probability that there are no aluminium washers drawn, when three washers are drawn at random from the box without replacement.
<pre><font size = 4 color ="indigo"><b>
There are 74+86 or 160 non-aluminum washers.  (This can also be calculated
by subtracting the 40 aluminum washers from the total 200, i.e., 200-40=160.)

 160 choose 3
--------------  =
 200 choose 3

{{{160C3/200C3 = 669920/1313400 = .5100654789}}}
</pre></font></b> 
c) Find the probability that there are two brass washers and either a steel or
an aluminium washer when three are drawn at random, without replacement.
<pre><font color="indigo" size = 4><b>
There are 74 brass washers.
There are 86+40 or 126 washers that are either steel or aluminum.
So the desired probability is

 (74 choose 2) + (126 choose 1)
--------------------------------  =
       200 choose 3

{{{(74C2+126C1)/(200C3) = (2701+126)/1313400 = 2827/1313400 =.020564946}}}

Edwin</pre>