isi maths 2009

[AJ]

hiii.. please help with these questions......

22. A student is browsing in a second-hand bookshop and finds n books of
interest. The shop has m copies of each of these n books. Assuming he never
wants duplicate copies of any book, and that he selects at least one book, how
many ways can he make a selection? For example, if there is one book of interest
with two copies, then he can make a selection in 2 ways.
A. (m + 1)^n − 1
B. nm
C. 2nm − 1
D. nm!/(m!)(nm−m)! − 1


12. Two persons, A and B, make an appointment to meet at the train station
between 4 P.M. and 5 P.M.. They agree that each is to wait not more than 15
minutes for the other. Assuming that each is independently equally likely to
arrive at any point during the hour, find the probability that they meet.
A 15/16
B 7/16
C 5/24
D 22/175

Answers are A and B respectively.....

[lovekesh]

For the first question...
Let there be m copies of a particular book.
No. of ways to select one book =1
No. of ways to select two books =1
..........
no. of ways to select m books =1
No. of ways to select 0 books =1
Therefore, total no of ways to select books(>=0) is m+1
Similarly for others.
If there are n types of books with each having m copies
Then no of way to select any no of book including zero is (m+1)^n
To select atleast one book, subtract the case where he selects zero book from each of these n books
so u get the answer.