00:01
In this question, we've given a certain club contains 10 men and 10 women, and a six -member committee consisting of two men and four women must be chosen from the club.
00:14
Now, take note that these two men and four women are selected without replacement.
00:24
And after they are selected, they are not arranged in any particular order within their own genders or they are slotted into any different titles.
00:33
So the order selection is not important.
00:41
So we'll be using combination.
00:47
That's the one with the c.
00:49
So number of possible committees would be from the 10 men, we will choose to.
00:58
Now, n in combinatorics is thumps or is plus.
01:04
N, so there's a thumps.
01:06
From the 10 women, we will choose for.
01:10
And so our answer is 9 450.
01:19
Now next one to find the number of possible committees if mr.
01:22
And mrs.
01:23
Smith refused to serve together on the committee.
01:26
Now there will be three mutually exclusive case, case one, or, all is plus case two or case three.
01:40
So let's look at the different cases.
01:42
Case one is where both are not serving in the committee case two mr smith is serving means mrs smith not serving case three mr smith is serving but mr smith is not okay let's look at case one both are not serving that means mr smith is not serving mrs smith is not serving so if both not serving there's only left with nine men and nine women to choose from.
02:52
So from the remaining nine men, i will choose two men and from the remaining nine women, i'm going to choose four.
03:02
And so this gives me 4536...