1. How many ways can I select 10 people to attend a conference if 4 must be Republicans and 6 must be Democrats if there are 10 Republicans and 15 Democrats?
15C6 x 10C4=
5005 x 210=
1,051,050
To solve this problem, we can use the combination formula. The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of people and r is the number of people we want to select.
In this case, we want to select 4 Republicans from a pool of 10 Republicans, and 6 Democrats from a pool of 15 Democrats. So, we would calculate the combinations separately and then multiply them to get the total number of ways to select both groups.
Step 1: Calculate the number of ways to select 4 Republicans from 10 Republicans.
C(10, 4) = 10! / (4!(10-4)!) = 10! / (4!6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210 ways
Step 2: Calculate the number of ways to select 6 Democrats from 15 Democrats.
C(15, 6) = 15! / (6!(15-6)!) = 15! / (6!9!) = (15 * 14 * 13 * 12 * 11 * 10) / (6 * 5 * 4 * 3 * 2 * 1) = 5005 ways
Step 3: Multiply the two results together to find the total number of ways to select both groups.
Total ways = 210 * 5005 = 1,051,050 ways
Therefore, there are 1,051,050 ways to select 10 people to attend the conference, with 4 Republicans and 6 Democrats.