)(15) You have identified eight courses that you are seriously considering takin
ID: 3321664 • Letter: #
Question
)(15) You have identified eight courses that you are seriously considering taking next term. a) How many ways are there to select three from among the eight without regard to order? Two of these are statistics courses, and you have definitely decided to take them (your friends are ready to have you committed!). How many ways are there now to select four courses to take? b) ) If you randomly select four from among the eight courses, what is the probability that both the statistics courses will be on your schedule?Explanation / Answer
(a)
Out of 8 courses, we have to select 3 courses from 8, without regard to order
= 8C3
= 56
(b)
Two of these 8 are statistics course
which you have to definitely take.
You have to select 4 courses,
then you have to select 2 out of the remaining 6 courses
No. of ways of selecting 4 courses in this way
= 6C2
= 15
(c)
If you randomly select 4 courses,
what is the probability that the 2 statistics courses will be selected?
No of ways to select 4 courses out of 8
= 8C4
= 70
No. of ways to select 4 courses such that 2 statistics courses are there
= 6C2
= 15
Thus, the required probability
= 15 / 70
= 3 / 14
= 0.2142857
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