December
1998 QUESTION 2 Total Marks: 20 Marks |
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| (a) | (i) In how many ways can a set of five different letters be selected from the English alphabet? | [1] |
| (ii) How many subsets with at least two elements does a set with six elements have? | [3] | |
| (iii) A group contains n men and n
women. How many ways are there to arrange these people in a row if the men and women
alternate?
|
[3] | |
| (b) | A tetrahedral die is one with four sides. The sides are numbered 1,2,3 and 4. When a tetrahedral die is thrown, the score is the number on the face which ends up face down. | |
| (i) Write down the sample space for the experiement consisting of throwing 2 tetrahedral dice. | [2] | |
| (ii) Write down the subset of the sample space corresponding to the event that the sum of the scores is 5. | [2] | |
| (iii) Calculate the possibility of
the event that the sum of the result is 5.
|
[2] | |
| (c) | A restaurant is doing a special "Dinner for Two Meal Deal". Customers choose any two different main courses from a selection of eight; any three different side dishes from a selection of ten and any two different deserts from a selection of six. | |
| (i) How many possible means can be chosen? | [4] | |
| (ii) Five of the main courses and one of the side dishes contain meat. If all possible combinations are equally likely to be chosen, what is the probability that the meal does not contain meat. | [3] |