SMSL/07
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT1301 Probability and Statistics I
Assignment 1
Section A
1. Out of 8 participants in a competition, 1 winner, 1 first runnerup and 1 second runnerup are
to be selected.
(a) Calculate the number of different ways to select the winner, first and second runnersup.
(b) Calculate the number of different possible combinations of the 5 losers.
2. How many distinguishable outcomes can be generated by rolling six identical dice simultane
ously,
(a) if the six faces of each die are numbered distinguishably?
(b) if each die has two red faces and four blue faces so that faces of the same colour are
indistinguishable?
3. A committee consisting of 1 president, 2 vice presidents, 2 secretaries and 10 general managers
are to be selected from 20 people. How many arrangements are possible?
4. Specify the outcome spaces and the corresponding outcome probabilities for the following ex
periments:
(a) a fair coin is tossed three times;
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 Spring '08
 SMSLee
 Statistics, Probability, fair coin, Mr. Chan, UNIVERSITY OF HONG KONG DEPARTMENT

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