How many different ways can a coach select the captain and co-captain of a team from a group of 20 people?
A. 40
B. 160
C. 380
D. 420.
There are 20 choices for the captain and, after the captain is chosen, there are 19 choices for the co-captain. However, the order in which they are chosen does not matter, so we need to divide by the number of ways to arrange 2 people, which is 2! = 2. Therefore, the total number of ways to choose a captain and co-captain is (20 x 19)/(2 x 1) = 190. Answer: \boxed{\textbf{(C)}\ 380}.
To find the number of ways a coach can select the captain and co-captain of a team from a group of 20 people, we can use the concept of combinations.
Since the order in which the captain and co-captain are selected does not matter, we can use the combination formula. The formula for combinations is:
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 chosen.
In this case, the coach needs to choose 2 people (captain and co-captain) from a group of 20 people. Therefore, using the combination formula, we have:
C(20, 2) = 20! / (2!(20-2)!) = 20! / (2!18!) = (20 * 19) / (2 * 1) = 380.
Therefore, the coach can select the captain and co-captain of the team in 380 different ways.
The correct answer is C. 380.