Apaint box contains 12 bottles of different colors. if we choose equal quantities of 3 different colors at random, how many color combinations are possible?

220 color combinations are possible.

Step-by-step explanation:

A combination is a way of selecting members from a grouping, such that the order of selection does not matter.

in our case we have 3-combinations of a set of 12 elements:

C(12, 3) = 12!/(3! (12-3)!)

C(12, 3) = 12!/(3! 9!)

C(12, 3) = (10*11*12)/(2*3)

C(12, 3) = 220 color combinations are possible.

220 combinations.

Step-by-step explanation:

This will be 12C3 combinations.

= 12! /  [(12-3)! 3!].

A quick mehtod to calculate this is  12*11*10 / 3*2*1

= 2*11*10

= 220.

part 1 answer = 8

part 2 answer = 72

step-by-step explanation:

part 1 explanation = add all of the numbers, then divide by how many numbers you have. so, 200/25 = 8.

part 2 explanation = not gonna lie, this is hard to explain, so just google how to do it.

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