1.

There are p copies each of n different subjects. Find the number of ways in which a nonempty selection can be made from them. Also find the number of ways in which at least one copy of each subject is selected.

Answer»

Solution :Number of WAYS of selection of zero or more copies of any subject =1+1+1+..+1 ((p+1) times) =p+1
So, total number of ways of selection of zero or more copies from all N subjects
=(p+1)(p+1)..(p+1)(n times)
`=(p+1)^(n)`
But this INCLUDES one CASE when no book is selected.
So, number of nonempty selections `=(p+1)^(n)-1`
Now number of ways of selection of at least one copy of any subject =1+1+1+..+1(p times )=p
So, number of ways in which at least one copy of each subject is selected `=pxxpxxpxx.xxp`(n times) `=p^(n)`.


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