A lock has n buttons labeled 1, 2, . . . , n. To open this lock
Question:
(1) 1,2,3
(2) 1,3,2
(3) 2, 1, 3
(4) 2, 3, 1
(5) 3, 1, 2
(6) 3, 2, 1
(7) {1,2}, 3
(8) 3, {1,2}
(9) {1,3}, 2
(10) 2, {1,3}
(11) {2, 3}, 1
(12) 1, {2, 3}
(13) {1,2, 3}.
[Here, for example, case (12) indicates that one presses button 1 first and then buttons 2, 3 (together) second.] (a) How many ways are there to press the buttons when n = 4? n = 5? How many for n in general? (b) Suppose a lock has 15 buttons. To open this lock one must press 12 different buttons (one at a time, or simultaneously in sets of two or more). In how many ways can this be done?
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Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
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