A company employs nine people and plans to select a group of six of these employees to receive advanced training. How many ways can the group of six employees be selected?

To find the number of ways the group of six employees can be selected, we can use the concept of combinations.

In this case, we need to select 6 employees out of 9, which means we want to find the number of combinations of 9 employees taken 6 at a time.

The formula to calculate combinations is given by:
C(n, k) = n! / (k! * (n-k)!)

Where:
- n is the total number of items (in this case, employees)
- k is the number of items to be selected (in this case, 6)
- n! is the factorial of n, which means multiplying all the numbers from 1 to n

Using this formula, we can calculate the number of ways to select the group of six employees:

C(9, 6) = 9! / (6! * (9-6)!)
= 9! / (6! * 3!)

Calculating this expression:

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
3! = 3 * 2 * 1 = 6

Plugging these values back into the formula:

C(9, 6) = 362,880 / (720 * 6)
= 362,880 / 4,320
= 84

Therefore, there are 84 ways the group of six employees can be selected.

To calculate the number of ways the group of six employees can be selected, we will use the formula for combinations.

The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)

Where:
- n is the total number of items (employees in this case)
- r is the number of items to be selected (group size in this case)
- ! denotes factorial

In this case, n = 9 (total number of employees) and r = 6 (group size).

Using the formula:
C(9, 6) = 9! / (6! * (9-6)!)

Calculating the factorial values:
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
(9-6)! = 3! = 3 * 2 * 1 = 6

Substituting the values into the formula:
C(9, 6) = 362,880 / (720 * 6)

Simplifying further:
C(9, 6) = 362,880 / 4,320

The number of ways the group of six employees can be selected is approximately 84.

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