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
Algebra.Com
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) (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.
RELATED QUESTIONS
A book shelf containing 20 books of which 12 are on circuit theory and 8 are on... (answered by stanbon)
A book shelf containing 20 books of which 12 are on circuit theory and 8 are on... (answered by stanbon)
Page Turner loves discrete mathematics. She has 7 "graph theory" books, 8 books about... (answered by sudhanshu_kmr)
three different language books, two different social science books and five mathematics... (answered by stanbon)
three different language books, two different social science books and five mathematics... (answered by stanbon)
3. Five English books and three Mathematics books are placed at random on a shelf. Find... (answered by ewatrrr)
Eight mathematics books and three chemistry books are to be placed on a shelf. In how... (answered by josmiceli)
Mr. Jones has 10 books that he is going to put on his bookshelf. Of these, 4 are... (answered by jrfrunner)
a. How many ways are there of arranging three different math books, five different... (answered by addingup)