Question

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
-
-
-
Ariel wants to choose 5 players for her basketball team. there are 7 players to choose from. how many different teams can ariel make?
A: 21
B: 35
C: 42
D: 56
-
-
-
((question in picture))
-
-
-

Answer 1

Explanation:

1. Number of peoples available to choose from = 20

`\text{Ways of selecting the captain from 20 people = }_(1)^(20)\textrm {C}=20`

After selecting the captain number of people left among which co captain can be selected = 20 - 1 = 19

`\text{Ways of selecting the co captain from 19 people = }_(1)^(19)\textrm {C}=19`

Hence, Number of ways a coach select the captain and co-captain of a team from a group of 20 people = 20 × 19 = 380

Therefore, The correct option is C. 380

2. Total number of players = 7

Number of players to be selected = 5

`\text{So, number of ways of selecting 5 players out of 7 = }_(5)^(7)\textrm {C}=21`

Therefore, The correct option is A. 21

3. Total number of outcomes = 20

The digits 1, 2, 3, 4, 5, 6 represent the student who make a C

Number of students who make a C at least 3 times = 13

`\bf\textbf{Required Probability = }(13)/(20)`

Therefore, The correct option is D

Answer 2

The coach can select the captain in 20 ways (i.e. from all the available 20 players), and he can select the co-captain in 19 ways (i.e. after selecting the captain, there will be 19 people left).
Therefore, the coach can select the captain and the co-captain in 20 x 19 = 380 ways.