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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
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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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.
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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