what is the percentage that 2 random people can be chosen from a total of 14 people.
To calculate the percentage that two random people can be chosen from a total of 14 people, we need to determine the total number of possible combinations of choosing two people from the group.
The formula for calculating combinations is:
C(n, r) = n! / (r! * (n - r)!),
where n is the total number of items and r is the number of items chosen at a time.
In this case, we have n = 14 (total number of people) and r = 2 (number of people chosen).
Using the formula, we can calculate the number of combinations:
C(14, 2) = 14! / (2! * (14 - 2)!)
= 14! / (2! * 12!)
= (14 * 13 * 12!)/(2 * 1 * 12!)
= (14 * 13) / (2 * 1)
= 182.
So, there are 182 possible combinations of choosing two people from a total of 14 people.
To find the percentage, divide the number of combinations by the total number of possible outcomes (which is the number of ways you can choose any two people from the group of 14). The total number of outcomes can be calculated using the same formula, but with r = 2 replaced by the total number of people in the group (n):
C(14, 2) = 14! / (2! * (14 - 2)!)
= 14! / (2! * 12!)
= (14 * 13 * 12!)/(2 * 1 * 12!)
= (14 * 13) / (2 * 1)
= 182.
So, the total number of outcomes is also 182.
To calculate the percentage, divide the number of combinations (182) by the total number of outcomes (182), and then multiply by 100 to get the percentage:
Percentage = (number of combinations / total number of outcomes) * 100
= (182 / 182) * 100
= 1 * 100
= 100%.
Therefore, the percentage that two random people can be chosen from a total of 14 people is 100%.