This question is about arrangements of buttons, which can be red, green or blue, in a line. Let u, be the number of distinct lines of n buttons which contain no two consecutive blue buttons. (i) Explain why uj = 3 and u2 = 8. (ii) Explain why any line of n buttons which contain no two consecutive blue buttons must be one of the two forms below. 00 n-2 buttons with no two consecutive blue buttons a red a blue button or a green button 0000 a red n-1 buttons with no two consecutive blue buttons or a green button (iii) Find un in terms of n.
This question is about arrangements of buttons, which can be red, green or blue, in a line. Let u, be the number of distinct lines of n buttons which contain no two consecutive blue buttons. (i) Explain why uj = 3 and u2 = 8. (ii) Explain why any line of n buttons which contain no two consecutive blue buttons must be one of the two forms below. 00 n-2 buttons with no two consecutive blue buttons a red a blue button or a green button 0000 a red n-1 buttons with no two consecutive blue buttons or a green button (iii) Find un in terms of n.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:This question is about arrangements of buttons, which can be red, green or blue, in a line.
Let u, be the number of distinct lines of n buttons which contain no two consecutive blue
buttons.
(i) Explain why uj = 3 and uz = 8.
(ii) Explain why any line of n buttons which contain no two consecutive blue buttons
must be one of the two forms below.
n-2 buttons with no two
consecutive blue buttons
a red
a blue
button
or a
green
button
0000
n-1 buttons with no two
consecutive blue buttons
a red
or a
green
button
(iii) Find un in terms of n.
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