How many different 5-person subcommittees can be formed from a club having 13 members?
To find the number of different 5-person subcommittees that can be formed from a club of 13 members, we can use the concept of combinations.
The formula for combinations is given by:
nCr = n! / (r! * (n-r)!)
Where "n" is the total number of items to choose from, and "r" is the number of items to choose.
In this case, we need to find the number of combinations when choosing 5 people from a pool of 13 members. Thus, we can calculate it using the formula.
n = 13 (total number of members)
r = 5 (number of people to choose)
Plugging these values into the formula, we have:
13C5 = 13! / (5! * (13-5)!)
Let's break down the calculations step by step:
1. Calculate the factorial of 13:
13! = 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
2. Calculate the factorial of 5:
5! = 5 * 4 * 3 * 2 * 1
3. Calculate the factorial of (13 - 5):
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
4. Substitute the values back into the original formula:
13C5 = 13! / (5! * 8!)
5. Calculate the final answer:
13C5 = (13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(5 * 4 * 3 * 2 * 1) * (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)]
After performing the calculations, we get the final answer:
13C5 = 1287
Therefore, there are 1287 different 5-person subcommittees that can be formed from a club having 13 members.