Permutation and Combination

Permutation combination is considered to be a hard topic by many GMAT aspirants. It is widely believed that questions from this topic appear when you score in the higher percentile levels in the GMAT Math section. If you have good understanding of the basics of this topic, it will be quite easy to crack questions that appear from permutation combination. 4GMAT's Math Lesson Book in this chapter covers the following areas

1. Independent Events, Product Rule, Sampling with and without replacement, sampling with and without ordering (arrangement).
2. Introduction to Permutation, combination. Difference between permutation and combination. Formulae associated with permutation and combination.
3. Examples of sampling with replacements, r-sequence and r-multisets.
4. Solved examples involving permutation and combination concepts in listing numbers
5. Solved examples involving re-arranging letters of words and their ranks
6. Concepts and solved examples on tossing of coins
7. Concepts and solved examples on rolling of a die and multiple dice
8. Solved examples on drawing one or more cards from a pack of cards
9. Typical permutation problems such as circular permutation, arranging boys and girls in a line etc.,
10. Typical combination problems such as questions on making musical albums, chess boards etc.,
11. About 5 illustrative examples to explain concepts; over 50 solved examples (with shortcuts wherever applicable to hard and tough questions) to acquaint you with as many different questions as possible; around 25 exercise problems with answer key and explanatory answers to provide you with practice and an objective type speed test with 50 questions. Explanatory answers and answer key are provided for the speed test.

Here is an example of a typical solved example in this chapter.
Sample Question
Question:
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

Explanatory Answer
There are three possible cases that will satisfy the condition of forming three letter passwords with at least 1 symmteric letter.

Case 1: 1 symmetric and 2 asymmetric or
Case 2: 2 symmetric and 1 asymmetric or
Case 3: all 3 symmetric

= {(11C1 * 15C2) + (11C2 * 15C1) + 11C3} * 3!

= {11 * permutation + permutation * 15 + permutation} x 6

= {1155 + 825 + 165} * 6

= 2145 * 6 = 12870