1. for each of the following, indicate whether it is a question that involves permutations, combinations, or neither, and then answer the question posed. explain your reasoning.
a. how many ways can a coach choose two co-captains from 16 players in the basketball team?
b. in how many ways can seven questions out of ten be chosen on an examination?
c. find the number of ways that 10 women in the finals of the skateboard street competition can finish first, second, and third in the x games final.
d. a postal zip code contains five digits. how many different zip codes can be made with the digits 0–9? assume a digit can be repeated.

Step-by-step explanation:

we are given some scenerios and we are to find out the total number of ways after mentioning permutations, combinations, or neither

a. How many ways can a coach choose two co-captains from 16 players in the basketball team?

Combination because both are having same position so order does not matter

16C2 = 120

b. In how many ways can seven questions out of ten be chosen on an examination?

Combinations because order of question does not matter.

10C7 = 10C3 = 120

c. Find the number of ways that 10 women in the finals of the skateboard street competition can finish first, second, and third in the X Games final.

Here order matters.  Hence permutation

10P3 = 720

d. A postal zip code contains five digits. How many different zip codes can be made with the digits 0–9? Assume a digit can be repeated.

Here repitition is allowed.  So neither permutation nor combination.

No of ways =

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional