from a group of six people two individuals are to be selected at random. How many possible selections are there?

"Selection" usually implies that the order does not matter, so

we have the number of ways of choosind 2 from 6
or C(6,2)
= 15

or

6x5 if we worry about order.
But we have to divide by 2 to eliminate all doubles of the kind AB and BA.

so 5x6/2 = 15

Well, if I were to pick two random people from a group of six, it would definitely be a clown-tastic show! Now, let's calculate the number of possible selections.

To do this, we'll use a combination formula. The formula for combinations is nCr = (n!)/(r!(n-r)!), where n is the total number of items and r is the number of items to be selected.

In this case, we have 6 people and we want to select 2 individuals, so it would be 6C2 = (6!)/(2!(6-2)!).

Let's simplify this expression!

6! (6 factorial) means multiplying all the positive integers from 6 down to 1:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.

Now let's calculate 2!:

2! = 2 x 1 = 2.

And let's calculate (6-2)!:

(6-2)! = 4! = 4 x 3 x 2 x 1 = 24.

Now let's plug these values back into the combination formula:

6C2 = (6!)/(2!(6-2)!) = (720)/(2 x 24) = 720/48 = 15.

So, there are 15 possible selections if we choose two individuals from a group of six. Enjoy the clown show!

To find the number of possible selections of two individuals from a group of six people, we can use the combination formula.

The combination formula is given by:

C(n, r) = n! / (r!(n-r)!)

Where n is the total number of items and r is the number of items selected.

In this case, we have 6 people, and we want to select 2 of them.

Plugging these values into the formula, we have:

C(6, 2) = 6! / (2!(6-2)!)

Simplifying further:

C(6, 2) = 6! / (2! * 4!)

The factorial (!) represents the product of all positive integers less than or equal to the given number.

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
2! = 2 * 1 = 2
4! = 4 * 3 * 2 * 1 = 24

Substituting these values back into the formula:

C(6, 2) = 720 / (2 * 24)
C(6, 2) = 720 / 48

Simplifying further:

C(6, 2) = 15

Therefore, there are 15 possible selections of two individuals from a group of six people.

To determine the number of possible selections from a group of six people when selecting two individuals at random, you can use the concept of combinations.

The formula for combinations is given by C(n, r) = n! / (r! * (n - r)!), where "n" represents the total number of objects (people in this case) and "r" represents the number of objects to be chosen (in this case, two individuals).

Plugging in the values, we have:
n = 6 (because there are six people)
r = 2 (because we want to select two individuals)

Using the formula, we can calculate the number of possible selections:
C(6, 2) = 6! / (2! * (6 - 2)!)
= 6! / (2! * 4!)
= (6 * 5 * 4!) / (2! * 4!)
= (6 * 5) / (2 * 1)
= 30 / 2
= 15

Therefore, there are 15 possible selections when choosing two individuals at random from a group of six people.