An Adviser has 9 products he wants to tell a client about, but only has time to tell him about 4. How many different ways can he give the details on 4 different products to the customer?
To determine the number of different ways the adviser can give details on 4 different products to the client, we can use the concept of combinations.
In this case, the adviser has 9 products to choose from, and he wants to select 4 products to discuss with the client.
The formula for the number of combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where n represents the total number of items to choose from (in this case, 9 products), and r represents the number of items to be selected (4 products).
Substituting the values into the formula:
C(9, 4) = 9! / (4!(9-4)!)
Simplifying further:
C(9, 4) = 9! / (4!5!)
Now, let's calculate the factorial values:
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
4! = 4 x 3 x 2 x 1 = 24
5! = 5 x 4 x 3 x 2 x 1 = 120
Replacing these values in the formula:
C(9, 4) = 362,880 / (24 x 120)
Simplifying further:
C(9, 4) = 362,880 / 2,880
Calculating the result:
C(9, 4) = 126
Therefore, the adviser can give details on 4 different products to the client in 126 different ways.
To find the number of different ways the adviser can give the details on 4 different products to the customer, we need to use the concept of combinations.
The formula for the number of combinations is:
C(n, r) = 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, the adviser wants to select 4 products out of 9, so n = 9 and r = 4.
Using the formula, we can calculate the number of different ways:
C(9, 4) = 9! / (4!(9-4)!) = 9! / (4!5!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126.
Therefore, the adviser can give the details on 4 different products to the customer in 126 different ways.