If you are making a team of 4 members. You have 4 women and seven men to choose from. How many different combinations can you have?
To calculate the number of different combinations you can have when forming a team of 4 members from a group of 4 women and 7 men, you can use the concept of combinations.
The formula to calculate combinations is:
nCr = n! / (r!(n-r)!)
Where n is the total number of items to choose from, r is the number of items to choose, and the exclamation mark (!) denotes the factorial of a number.
In this case, you have 4 women and 7 men. You need to choose a team of 4 members.
Using the combination formula, the calculation would be:
nCr = (4+7)C4 = 11C4
Now, let's calculate this step by step:
Step 1: Calculate the factorial of 11 (11!) - which means multiplying all the numbers from 1 to 11 together.
11! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 = 39,916,800
Step 2: Calculate the factorial of 4 (4!) - which means multiplying all the numbers from 1 to 4 together.
4! = 1 * 2 * 3 * 4 = 24
Step 3: Calculate the factorial of 7 (7!) - which means multiplying all the numbers from 1 to 7 together.
7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5,040
Step 4: Plug these values into the combination formula:
nCr = 11! / (4! * (11-4)!)
= 39,916,800 / (24 * 5,040)
= 39,916,800 / 120
= 332,640
Hence, you can have 332,640 different combinations when forming a team of 4 members from a group of 4 women and 7 men.