# Counting (2nd Edition) by Koh Khee Meng, Tay Eng Guan

By Koh Khee Meng, Tay Eng Guan

Publication Description

Publication Date: January 25, 2013

This e-book in its moment variation is an invaluable, appealing creation to easy counting suggestions for higher secondary to undergraduate scholars, in addition to academics. more youthful scholars and lay those that enjoy arithmetic, let alone avid puzzle solvers, also will locate the booklet attention-grabbing. some of the difficulties and functions listed below are strong for increase talent in counting. also they are worthwhile for honing uncomplicated abilities and methods more often than not challenge fixing. some of the difficulties keep away from regimen and the diligent reader will usually observe a couple of means of fixing a selected challenge, that's certainly an enormous know-how in challenge fixing. The ebook therefore is helping to provide scholars an early begin to studying problem-solving heuristics and pondering skills.

New chapters initially from a supplementary e-book were extra during this variation to considerably elevate the insurance of counting concepts. the hot chapters comprise the primary of Inclusion and Exclusion, the Pigeonhole precept, Recurrence kinfolk, the Stirling Numbers and the Catalan Numbers. a couple of new difficulties have additionally been extra to this edition.

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**Additional info for Counting (2nd Edition)**

**Sample text**

Find the number of ways in which this can be done, (b) It was decided that 2 of the 7 women must either be selected together or not selected at all. Find how many possible teams could be selected in these circumstances. The selected team is arranged into 4 pairs, each consisting of a man and a woman. Find the number of ways in which this can be done. ,n-. This page is intentionally left blank Chapter 5 The Bijection Principle We have introduced three basic principles for counting, namely, the (AP), the (MP) and the (CP).

6 ^ T Counting 40 segments. 6. How many shortest P—Q routes in the grid are there? Solution Certainly, we can solve the problem directly by listing all the possible shortest routes. This, however, would not be practical if we wish to solve the same problem in, say, a 190 x 100 rectangular grid. We look for a more efficient way. There are two types of segments: horizontal and vertical. Let us use a "0" to represent a horizontal segment, and a " 1 " to represent a vertical segment. 6 can accordingly be represented by the binary sequence with four "0"s and two "l"s as shown below: -> 010100 P •- Likewise, we can have: _J -> 000101 and so on.

4 of Balls into Boxes 51 Six distinct symbols are transmitted through a communication channel. A total of 18 blanks are to be inserted between the symbols with at least 2 blanks between every pair of symbols. In how many ways can the symbols and blanks be arranged? This page is intentionally left blank Chapter 7 More Applications of (BP) We shall give additional examples in this chapter to show more applications of (BP). Consider the following linear equation: xi + x2 + x3 = 7. (1) If we put x\ = 4, X2 = 1 and x% = 2, we see that (1) holds.