Question

A teacher decides to award exam grades A, B, or C by a new method. Out of 20 children, three are to receive A's, five B's and the rest C's. She writes the letters A, B and C on 20 pieces of paper and invites the pupils to draw their exam result, going through the class in alphabetical order. Find the probability that the first three pupils all get different grades.

Answer 1

There are 3 A's, 5 B's and 12 C's

a)Probability that first gets A = 3/20
When first has got A, then there are 19 pieces of paper in which there are 2 A's
Therefore, probability that second gets A = 2/19
When second also has got A, then there are 18 pieces of paper in which there is 1 A.
Therefore probability that third gets A = 1/18

Therefore probability that first three get A's
= 3/20 * 2/19 * 1/18
= 1/1140

b)Probability that first gets A = 5/20 = 1/4
When first has got B, then there are 19 pieces of paper in which there are 4 B's
Therefore, probability that second gets B = 4/19
When second also has got B, then there are 18 pieces of paper in which there are 3 B's.
Therefore probability that third gets B = 3/18 = 1/6

Therefore probability that first three get B's
= 1/4 * 4/19 * 1/6
= 1/114

c)Probability that first gets A = 3/20
Probability that second gets B = 5/19
Probability that third gets C = 12/18 = 2/3
Combined probability of above three events = 3/20 * 5/19 * 2/3
= 1/38
If their grades are shuffled among themselves, then also they will have different grades. The grades of first three can be shuffled in 3! = 6 ways.
Therefore probability that first three get different grades = 1/38 * 6 = 3/19

d) In (b), we calculated that the probability first three get B = 1/114
When first three have got B, then there are 17 pieces of paper in which there are 2 B's.
Therefore probability that fourth gets B = 2/17
Therefore probability that first four get B
= 1/114 * 2/17
= 1/969


http://answers.yahoo.com/question/index?qid=20081111194410AAjyuMz

ok @Faris_Waleed

Answer 2

I don't understand part (c)

Answer 3

which line?

Answer 4

This one: c)Probability that first gets A = 3/20
Probability that second gets B = 5/19
Probability that third gets C = 12/18 = 2/3
Combined probability of above three events = 3/20 * 5/19 * 2/3
= 1/38
If their grades are shuffled among themselves, then also they will have different grades. The grades of first three can be shuffled in 3! = 6 ways.
Therefore probability that first three get different grades = 1/38 * 6 = 3/19

Answer 5

no, which statement??

Answer 6

The one which is talking about the grades of first three can be shuffled in 3!= 6 ways

I don't understand why did we do this 3!

Answer 7

shuffled means http://www.google.co.in/#hl=en&output=search&sclient=psy-ab&q=shuffled&oq=shuffled&gs_l=hp.3..0l4.65070.65070.0.65649.1.1.0.0.0.0.270.270.2-1.1.0.les%3B..0.0...1c.1.zWKo12X_ynw&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&fp=959a9b2926790dbd&bpcl=38625945&biw=1280&bih=677

Answer 8

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