00:01
In this problem, it is said that from a group of 13 boys and 10 girls, a committee of five students is chosen at random.
00:09
Now, in the first subpart, we need to determine the probability that all five members on the committee will be girls.
00:16
So the probability is the number of favorable outcomes divided by the total number of outcomes.
00:21
First of all, let us consider the total number of outcomes, which you write in the denominator.
00:25
So there are 13 boys and 10 girls.
00:28
So that's 13 plus 10, which is 23 students in total.
00:33
And out of those 23 students, any 5 students need to be selected at random to form the committee.
00:39
So this can be done in 23c5 ways.
00:42
Here we use c, which represents combination.
00:45
And we use combination and not permutation in this case because the order of selection of the students does not matter.
00:51
So that's the total number of outcomes.
00:53
Next, let us consider the number of favorable outcomes, which we write in the numerator.
00:58
So the number of favorable outcomes will be the number of ways we can choose all five members of the committee to be girls.
01:04
So there are a total of 10 girls.
01:07
Out of those 10 girls, if we select any 5, then that will mean we have selected all 5 members for the committee to be girls.
01:14
And this can be done in 10c5 ways.
01:17
So 10c5 is 10 factorial by 5 factorial times the factorial of 10 minus 5, which is 5.
01:23
23c5 is 23 factorial by 5 factorial times the factorial of 23 minus 5, which is equal to 18...