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# Question: combinatorics and basic probability and combinatorics and basic probabilities the...

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Combinatorics and basic probability, and Combinatorics and basic probabilities

(The answers for to the following questions may be given in the index form or as exact fractions or as decimal rounded to 6 decimal places .)

In a short survey conducted in one of the secondary schools in Melbourne, all year 7 students were asked to rate their overall satisfaction with on-line learning using the score between 1 and 5 (1 being the lowest score).

(a) What is the total number of different combinations of the scores that may be recorded for 8 randomly selected students?

(b) What is the probability of not recording all 8 lowest scores for 8 randomly selected students.

(c) What is the probability of recording exactly 1 lowest score for 8 randomly selected students? To answer this question follow the steps:

(i) What is the number of different combinations of the scores recordings assumed that out of 8 students the first one has recorded the lowest score and the scores of remaining 7 students were not 1.

(ii) In how many different ways we can choose one students who recorded the lowest score out of group of 8 students?

(iii) What is the number of different combinations of the scores with exactly 1 lowest score?

(iv) So what is the probability of recording exactly 1 lowest score for 8 randomly selected stu- dents?

(d) By following the steps similar to part (c), find the probability of recording exactly 3 lowest scores 8 randomly selected students?

The survey yields the following results: out of 50 of all year 7 students in this school 15 students are satisfied with the on-line learning (they have selected scores 4 or 5) and the rest of the students are not satisfied (they selected score 1 or 2 or 3).

(e) What is the probability that out of 5 randomly select students all 5 students are satisfied with the on-line learning.

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