A group of 4 journalists are chosen to cover a news story. There are 6 male journalists and 8 female journalists available to be selected for the group.How many possible groups can be formed if the group consists of exactly 2 men and 2 women?
Question
A group of 4 journalists are chosen to cover a news story. There are 6 male journalists and 8 female journalists available to be selected for the group.How many possible groups can be formed if the group consists of exactly 2 men and 2 women?
Solution
To solve this problem, we can use the combination formula which is nCr = n! / [(n-r)! * r!], where n is the total number of options, r is the number of options chosen, and "!" denotes a factorial.
First, we calculate the number of ways to choose 2 men from 6. This is represented as 6C2:
6C2 = 6! / [(6-2)! * 2!] = (65) / (21) = 15
Next, we calculate the number of ways to choose 2 women from 8. This is represented as 8C2:
8C2 = 8! / [(8-2)! * 2!] = (87) / (21) = 28
Finally, we multiply these two results together to find the total number of possible groups. This is because for each way of choosing the men, there are multiple ways of choosing the women.
So, the total number of possible groups is 15 * 28 = 420.
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