GMAT Quant | Permutation Q11

This sample GMAT Math question is a Permutation problem solving question. The concept tested is to find the number of ways of selecting an object from identical objects. A GMAT 650 level, interesting permutation combination question.

Question 11: There are 4 identical pens and 7 identical books. In how many ways can a person select at least one object from this set?

1. 12
2. (2⁴ – 1)(2⁷ – 1)
3. 11
4. 2¹¹ - 1
5. 39

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Video Explanation

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Explanatory Answer | GMAT Selection from Identical Objects

Step 1 of solving this GMAT Permutation Question: Understanding the premise

What if the 4 pens were distinct?
If the pens are distinct, the number of ways of selecting one pen is 4 ways.
If the pens are identical, the number of ways of selecting a pen is 1 way, as all of them are the same.
If the pens are distinct, the number of ways of selecting two pens is 4C₂ ways.
If the pens are identical, the number of ways of selecting two pens is 1.
This information is key to how we approach the problem.

Step 2 of solving this GMAT Permutation Question: Selecting at least one object

We can select anything from 0 to 4 pens.
Therefore, 0 or 1 or 2 or 3 or 4 pens can be selected in 5 ways.
Similarly, we can select from 0 to 7 books.
Hence, 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 pens can be selected in 8 ways.

The number of ways of selecting none or all of the available objects is 8 × 5 = 40 ways.

However, we have to select at least one object from these two.
Hence, the possibility of selecting 0 books and 0 pens has to be subtracted from the overall possibilities.
∴ 40 - 1 = 39 ways.

Choice E is the correct answer.