Permutation Combination : Selecting from non distinct object

Here is a question on selecting one or more objects from a set of object, all of which are not distinct.

Question

There are 4 identical pens and 7 identical books. In how many ways can a person select at least one object from this set?
a. 12
b. (2⁴ - )(2⁷ -1)
c. 11
d. 2¹¹ - 1
e. 39

Correct Answer : Choice E. 39 ways.

 

Explanatory Answer

A person can select none or up to 4 identical pens in 5 ways (0 or 1 or 2 or 3 or 4).

A person can select none or up to 7 identical books in 8 ways (0 or 1 or 2 or .. 7).

So, a person can select none or all of the objects in 5 * 8 = 40 ways.

However, in one case neither a pen nor book would have got selected. We need to select at least one object.

Therefore, number of ways = 40 - 1 = 39.