<p>hi.
can someone pleaaaaaase copy here the Official SAT Question Of The Day of 10th May
along with the answer and answer explanation?!! thanks a ton!</p>
<p>Of 5 employees, three are to be assigned an office and 2 are to be assigned a cubicle. If 3 of the employees are men and 2 are women, and if those assigned an office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?</p>
<p>(A) 1 over 3
(B) 2 over 5
(C) 1 over 2
(D) 3 over 5
(E) 2 over 3</p>
<p>D. 3/5
Of the 5 office workers, 3 are to be assigned an office. This is an example of combinations: to find the number of ways of choosing 3 of the 5 workers, you can count the number of ways of selecting the workers one at a time and then divide by the number of times each group of 3 workers will be repeated.</p>
<p>There are 5 ways of choosing the first worker to get an office. Then there will be 4 ways of choosing the second worker to get an office, and 3 ways of choosing the third worker. This is a total of 5 times 4 times 3 = 60 possibilities. In these 60 possible selections, each distinct group of 3 workers will occur 3 times 2 times 1 = 6 times. (There are 3 possibilities for the first worker chosen from the group, 2 for the second worker chosen, and only 1 for the third.) Therefore, there are 60 over 6 = 10 different ways the 3 workers who get an office can be chosen from the 5 workers.</p>
<p>How many of these 10 possible groups of 3 workers consist of 2 men and 1 woman? From the 3 male workers, 2 can be chosen in 3 different ways. There are 2 possibilities for the female worker. Therefore, 3 times 2 = 6 of the groups of 3 workers consist of 2 men and 1 woman.</p>
<p>Since there are 10 different ways the 3 workers who get an office can be chosen, and 6 of these possible groups of 3 workers consist of 2 men and 1 woman, the probability that the offices will be assigned to 2 men and 1 woman is 6 over 10, or 3 over 5.</p>
<p>[The</a> Official SAT Question of the Day](<a href=“http://sat.collegeboard.com/practice/answered-question-of-the-day?src=E&questionId=20110510&answerCd=D&ep_ch=QD&ep_mid=7591026&ep_rid=1362268]The”>http://sat.collegeboard.com/practice/answered-question-of-the-day?src=E&questionId=20110510&answerCd=D&ep_ch=QD&ep_mid=7591026&ep_rid=1362268)</p>
<p>Of 5 employees, three are to be assigned an office and 2 are to be assigned a cubicle. If 3 of the employees are men and 2 are women, and if those assigned an office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?</p>
<p>(A) 1 over 3
(B) 2 over 5
(C) 1 over 2
(D) 3 over 5
(E) 2 over 3 </p>
<p>I assume you know how to use the nCr button on your calculator (if not, tell me and I’ll explain).</p>
<p>Step 1: Find the total number of ways to assign people to offices - This is 5C3 = 10.
Step 2: Find the number of successes - (3C2)(2C1) = 3*2=6.</p>
<p>Probability = success/total = 6/10 = 3/5, choice (D).</p>
<p>Remarks:</p>
<p>(1) We use combinations because it doesn’t matter what order we assign the employees to offices.
(2) In the formula nCr, n is the total we are choosing from, and r is the number we are choosing. For example, 3C2 represents the fact that we are choosing 2 men from a total of 3 men.</p>
<p>Takes longer but might be more intuitive for some (and is certainly better than the ridiculous College Board explanation)…</p>
<p>How many ways can the 3 offices be filled to meet the requirement of the question?</p>
<p>M and M and W
or
M and W and M
or
W and M and M</p>
<p>As you know, ‘and’ = multiply and ‘or’ = add. Just fill in the probability of each individual event…</p>
<p>(3/5) * (2/4) * (2/3)
+
(3/5) * (2/4) * (2/3)
+
(2/5) * (3/4) * (2/3)</p>
<p>=</p>
<p>12/60
+
12/60
+
12/60</p>
<p>=36/60 or 3/5</p>
<p>@ DrSteve — please enlighten me about the usage of the nCr button and of the situations where it can be used. thanks!</p>
<p>@DrSteve – could ya please apprise me of the nCr function? i dont know about it cuz all of the SAT practise tests I have given till now have been without the help of calculator. Also, could you tell some other functions on the calculator/ strategies by which questions can be easily solved without making a mess on the booklet using the calculator?</p>