00:01
In this problem, it is said that a subcommittee of seven needs to be chosen from a senate committee of seven democrats and seven republicans.
00:08
Now, in the first problem, we need to determine in how many ways we can do that if all members are eligible.
00:15
So the committee has seven democrats and seven republicans.
00:19
That's a total of 14 people.
00:21
7 plus 7, 14 people.
00:24
And out of them, we need to select any seven people at random to form the subcommittee.
00:29
And this is because all members are eligible so we can choose any seven out of those 14 people.
00:35
And this can be done in 14c7 ways.
00:38
Here we use c, which represents combination.
00:41
And we use combination and not permutation in this case because the order of selection of the people does not matter.
00:47
So this is 14 factorial by 7 factorial times the factorial of 14 minus 7, which is 7...