Jasmine had 4 bulbs: green, orange, brown ,purple. how many ways can hang so green and brown are not next to each other

There are 4! ways in which she can hang the bulbs, which means 4x3x2x1. this is 24 ways.
g o b p
g o p b
g b p o
g b o p
g p o b
g p b o
o g b p
o g p b
o p g b
o p b g
o b p g
o b g p
b o g p
b o p g
b p o g
b p g o
b g o p
b g p o
p g o b
p g b o
p b o g
p b g o
p o b g
p o g b

of these ways, there are 12 where green and brown aren't next to each other

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: multiply exponents per exponent rules to get: remember you subtract exponents from the denominator and add exponents in the numerator so: simplify further: so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.