Question

There are 11 patients in Dr. Wooten's waiting room. Dr. Wooten can see 7 patients before lunch. In how many orders can she see 7 of the 11 patients before lunch?

a) 330
b) 7920
c) 77
d) 1,663,200

Answer 1

Dr. Wooten can see 7 out of 11 patients before lunch in 330 different orders based on the combination formula C(n, k) = n! / (k! * (n - k)!), where n is the total number of items and k is the number of items to be chosen.

Step-by-step explanation:

The question involves calculating the number of ways in which Dr. Wooten can see 7 out of the 11 patients before lunch. This is a classic combinatorics problem that can be solved using the concept of combinations since the order in which the patients are seen does not matter.

The formula for combinations is given by:

C(n, k) = n! / (k! * (n - k)!)

Where:

• n is the total number of items (in this case, patients).
• k is the number of items to choose (in this case, patients to be seen before lunch).

Using the formula:

C(11, 7) = 11! / (7! * (11 - 7)!) = 11! / (7! * 4!) = 330

Therefore, Dr. Wooten can see the patients in 330 different orders before lunch.