A company employs six people and plans to select a group of two of these employees to receive advanced training. How many ways can the group of two employees be selected?
Well, selecting a duo can be quite a handful! Let's see how many ways we can tickle these employees' fancy.
To determine the number of ways to select a group of two employees out of six, we can use a little mathematical trickery called combinations.
In this case, the formula for combinations can save the day, and it goes like this:
nCr = n! / ((n - r)! * r!)
Where n represents the total number of employees, and r represents the number of employees we want to select.
So, plugging in the values, we have:
6C2 = 6! / ((6 - 2)! * 2!)
Doing some number juggling, we get:
6C2 = 6! / (4! * 2!)
And after simplifying further:
6C2 = (6 * 5) / (2 * 1)
Finally, calculating the expression, we find:
6C2 = 15
Voila! There are 15 ways to select a group of two employees out of six. So, the company can choose to pair them up in a whopping 15 different combinations. Isn't that clownishly creative?
To find the number of ways to select a group of two employees out of six, we can use the combination formula, also known as "n choose r."
The formula for the number of ways to choose r items out of a set of n items is given by:
nCr = n! / r!(n - r)!
In this case, we have n = 6 (six employees) and r = 2 (group of two employees).
Plugging these values into the formula, we get:
6C2 = 6! / 2!(6 - 2)!
= 6! / 2!4!
= (6 * 5 * 4!) / 2!4!
= (6 * 5) / 2!
= 30 / 2
= 15
Therefore, there are 15 ways to select a group of two employees out of six.
To determine the number of ways to select a group of two employees out of six, we can use the concept of combinations.
A combination is a selection of items without regard to the order in which they are arranged. In this case, we want to know the number of ways to select two employees out of six, without considering the arrangement of the selected employees.
The formula for calculating combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n represents the total number of items to choose from and r represents the number of items to be selected.
In this case, we have six employees (n = 6) and we want to select two employees (r = 2).
Plugging the values into the formula, we can calculate the number of ways to select a group of two employees:
C(6, 2) = 6! / (2! * (6 - 2)!)
Calculating this expression:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
2! = 2 * 1 = 2
4! = 4 * 3 * 2 * 1 = 24
C(6, 2) = 720 / (2 * 24) = 720 / 48 = 15
Therefore, there are 15 ways to select a group of two employees out of the six.
choose 2 from 6
= C(6,2)
= 6!/(4!2!) = 15