Question 247120
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.