Counting by Khee Meng Koh & Eng Guan Tay

Author:Khee Meng Koh & Eng Guan Tay [Koh, Khee Meng & Tay, Eng Guan]
Language: eng
Format: epub
Tags: mathematics, General, Graphic Methods, Combinatorics
ISBN: 9789814401906
Google: N1_uuQAACAAJ
Publisher: World Scientific
Published: 2013-09-15T20:43:54+00:00

(i) divisible by at least one of 2, 3 and 5;

(ii) divisible by none of 2, 3 and 5.

13.5 Seven distinct objects are to be put into three distinct boxes. Find the number of ways this can be done if

(i) there is no restriction;

(ii) no box is empty.

13.6 The following figure shows a 5 by 8 rectangular grid with two specified corners p and q and three specified segments ab, cd and ef. Find in the grid

(i) the number of shortest p-q routes;

(ii) the number of shortest p-q routes that pass through at least one of the segments ab, cd and ef;

(iii) the number of shortest p-q routes that do not pass through any of the segments ab, cd and ef.

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