Answer:
a) 16.7% probability that E will speak first.
b) 3.33% probability that C will speak fifth and B will speak last.
c) 0.14% probability that the students will speak in the following order: DECABF.
d) 33.33% probability that A or B will speak first.
Step-by-step explanation:
The first speaker can be any of them. The second can be any of them bar the first. It continues until the last one. So the total number of outcomes is 6! = 720.
(a) E will speak first
The first one to speak is E.
The other five can be selected in any order. So there are 5! = 120 total outcomes in which E speaks first.
There is a 120/720 = 0.167 probability that E will speak first.
(b) that C will speak fifth and B will speak last
The fifth can only be C and the sixth can only be B.
The first four can be selected in any order. So there are 4! = 24 outcomes in which C speaks fifth and B last.
There is a 24/720 = 0.0333 probability that C will speak fifth and B will speak last.
(c) that the students will speak in the following order: DECABF
This is the only possible outcome in this order.
So there is a 1/720 = 0.0014 = 0.14% probability that the students will speak in the following order: DECABF.
(d) that A or B will speak first.
For A first, the following five can be in any order. So there are 5! = 120 outcomes in which A speaks first. The same logic and result for B.
So there are 240 outcomes in which A or B speaks first.
There is a 240/720 = 0.3333 = 33.33% probability that A or B will speak first.
