SOLUTION: A book shelf containing 20 books of which 12 are on circuit theory and 8 are on Mathematics. If three books are taken out at random, find the probability that all the three are on

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Question 247120: A book shelf containing 20 books of which 12 are on circuit theory and 8 are on Mathematics. If three books are taken out at random, find the probability that all the three are on the same subject.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
20 books.
12 on circuit theory.

8 on mathematics.

you pick 3 at random.

probability that all 3 are on circuit theory would be 12/20 * 11/19 * 10/18

probability that all 3 are on mathematics would be 8/20 * 7/19 * 6/18

probability that all 3 are either on circuit theory or on mathematics would be:

(12/20 * 11/19 * 10/18) + (8/20 * 7/19 * 6/18)

you can see this with smaller numbers.

assume 5 books total.

3 on circuit theory
2 on math

you pick 2 at random.

probability all on circuit theory is 3/5 * 2/4 = 6/20

probability all on math is 2/5 * 1/4 = 2/20

probability either all circuit theory or all math is 6/20 + 2/20 = 8/20

let abcde be the books.

possible permutations of 2 are:
ab
ac
ad
ae
ba
bc
bd
be
ca
cb
cd
ce
da
db
dc
de
ea
eb
ec
ed

assume abc are books on circuit theory

look for all permutations of ab or ac or bc

that would be ab ba ac ca bc cb

that should be 6 occurrences out of 20

assume de are books on math.

look for all permutations of de

that would be de and ed

that should be 2 occurrences out of 20

total possible occurrences is 8 / 20 which is the same as derived above.