Here is a question on selecting one or more objects from a set of object, all of which are not distinct.
There are 4 identical pens and 7 identical books. In how many ways can a person select at least one object from this set?
b. (24 - )(27 -1)
d. 211 - 1
Correct Answer : Choice E. 39 ways.
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.
Labels: GMAT Counting Methods, GMAT Permutation Combination, GMAT Problem Solving, GMAT Problem Solving Practice