(a) Consider a group of four students. Each student has a favourite colour, which can be any one of the colours of the rainbow (red, orange, yellow, green, blue, indigo, violet), assuming that each colour is equally likely as a favourite colour. What is the probability that no two students have the same favourite colour? (b) Consider a group of seven students. Each student has a favourite colour, which can be any one of the seven colours of the rainbow (assuming again that each colour is equally likely as a favourite color). i. What is the probability that no two students have the same favourite colour? ii. What is the probability that some of them have the same favourite colour?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Consider a group of four students. Each student has a favourite colour, which can
be any one of the colours of the rainbow (red, orange, yellow, green, blue, indigo,
violet), assuming that each colour is equally likely as a favourite colour.
What is the probability that no two students have the same favourite colour?
(b) Consider a group of seven students. Each student has a favourite colour, which
can be any one of the seven colours of the rainbow (assuming again that each
colour is equally likely as a favourite color).
i. What is the probability that no two students have the same favourite colour?
ii. What is the probability that some of them have the same favourite colour?
Transcribed Image Text:(a) Consider a group of four students. Each student has a favourite colour, which can be any one of the colours of the rainbow (red, orange, yellow, green, blue, indigo, violet), assuming that each colour is equally likely as a favourite colour. What is the probability that no two students have the same favourite colour? (b) Consider a group of seven students. Each student has a favourite colour, which can be any one of the seven colours of the rainbow (assuming again that each colour is equally likely as a favourite color). i. What is the probability that no two students have the same favourite colour? ii. What is the probability that some of them have the same favourite colour?
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