a jury of people is chosen from 10 men and 12 women. How many ways can a jury of 6 men and women be chosen?
You said "How many ways can a jury of 6 men and women be chosen?"
I am sure you meant to say
"How many ways can a jury of 6 men and 6 women be chosen?"
That would be C(12,6)xC(10,6)=....
If you meant it the way you said it, then it would be more difficult.
Do it with different cases
6 women, no men --> C(12,6)xC(10,0)=924
5 women, 1 man ---> C(12,5)xC(10,1)=7920
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1 woman, 5 men --> C(12,1)xC(10,5)=3024
no woman, 1 man--> C(12,0)xC(10,6)=210
Now add them all up.
12608
Well, let's see. There are 10 men and 12 women, which means there's a total of 22 people. We need to choose 6 men and women for the jury.
To calculate the number of ways, we'll first find the number of ways to choose 6 men from the 10 available. This can be calculated using the formula for combinations: C(n, r) = n! / (r!(n-r)!). So, C(10, 6) = 10! / (6!(10-6)!) = 210.
Next, we'll find the number of ways to choose 6 women from the 12 available: C(12, 6) = 12! / (6!(12-6)!) = 924.
To find the total number of ways, we multiply these two results together: 210 * 924 = 194,040.
So, there are 194,040 different ways to choose a jury of 6 men and women from the available selection. That's a lot of potential juries!
To solve this problem, we will use the concept of combinations, specifically the "nCr" formula, where "n" represents the total number of people to choose from, and "r" represents the number of people we want to choose.
In this case, we want to choose a jury of 6 men and women from a total of 10 men and 12 women. The number of ways to do this can be calculated using the formula:
nCr = n! / (r!(n-r)!)
Here, "!" denotes the factorial function. The factorial of a number is the product of all positive integers less than or equal to that number.
Using the formula, the number of ways to choose 6 men and women from a group of 10 men and 12 women can be calculated as follows:
10C6 * 12C0
10C6 = 10! / (6!(10-6)!) = (10 * 9 * 8 * 7)/(4 * 3 * 2 * 1) = 210
12C0 = 12! / (0!(12-0)!) = 1
Therefore, the total number of ways to choose a jury of 6 men and women from the given group is:
210 * 1 = 210
So, there are 210 ways to select a jury of 6 men and women from a pool of 10 men and 12 women.