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

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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. (2^{4} - )(2^{7} -1)

c. 11

d. 2^{11} - 1

e. 39

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Correct Answer : Choice E. 39 ways.

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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.

a. 12

b. (2

c. 11

d. 2

e. 39

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