00:01
So since we know that these 10 people are all getting different scores.
00:08
So we could imagine this question as assigning the 10 person with 10 seats.
00:14
And the sequence of the seats are decided by their score ranking.
00:20
So this means that the first seat is given by the people who rank the first.
00:28
And the second seed is given by the people who rank the second, and so on.
00:36
So now we compute the probability of x equals to 1, which means that the first seed is occupied by a female.
00:48
And how to assign this seed, we can first look at the group of the men.
00:54
So we know that there are five men.
00:57
So assigning the five men, there are five factorial, for the amount of five men.
01:05
And for assigning the five women, there are also five factorial.
01:12
And now we assign the two groups together.
01:18
Now we know that the first seat must be occupied by a female.
01:22
So this is determined.
01:24
And for the other four female, there are four female left.
01:30
And we know that since the four female first place is occupied by a female so there are nine seats left for the nine left seats they must be occupied by four of the so the four females can choose freely from the nine seats left so we are getting nine of nine of four here so we times so we times these three these three numbers together this is all the possible sequences for the seeds for x equals to one and now we look at the denominator so we look at if we don't have the restraint that the first place must be occupied by a woman then there are 10 factorial for the for the 10 people so computing this probability of x equals to 1, which is equal to a half.
02:43
And now we look at the second term, which is probability of x equals to, x equals to 2.
02:54
And which means that a woman is occupying the highest score of the woman is occupying the second place.
03:07
So this means that the first place must be occupied by a man.
03:15
And the women can only choose from, and since we know that the highest woman is only getting the second place, so there are eight seats left from the second place to the end.
03:38
And there are four women left.
03:42
Who can choose freely from the eight seats.
03:47
So we have eight of four here.
03:51
And also we assign the sequence among the man group, and we assign the seats among the women group...