The question is not clear as whether she needs to have a pair of each color in the drawer or outside the drawer.

The question would be more logical if she wants to have a pair of each color outside the drawer i.e. to use any pair of them. Then the answer will be 3. As the minimium number of pairs will be, first time red pair, second time black pair and then white pair.

OR, the question may want to say she wants to leave only different pairs of socks in the drawer. So the answer will be 6, which is not found in the answers.

Please check the question as it is not clear at all.

I understood it as Melissa needs to have a pair of red, a pair of black and a pair of white socks.
This is one of those "minimum" question that need to be solved this way:
She will need to get all of 5 pairs of white socks, then all 3 pairs of red socks and only 1 pair of black socks in order to make sure she gets at least one pair of each.
So, 5+3+1=9

hijazim wrote:The question is not clear as whether she needs to have a pair of each color in the drawer or outside the drawer.

The question would be more logical if she wants to have a pair of each color outside the drawer i.e. to use any pair of them. Then the answer will be 3. As the minimium number of pairs will be, first time red pair, second time black pair and then white pair.

OR, the question may want to say she wants to leave only different pairs of socks in the drawer. So the answer will be 6, which is not found in the answers.

Please check the question as it is not clear at all.

to ensure what is asked, to be inside the drawer only, she doesn't even need to touch the drawer, my dear friend! now what says any common sense, go with that.

On a good day she would only need 3 draws (1 for red, 1 for black and 1 for white)

But in the worst case scenario,

first pairs she draws will be White
2nd pair - White
3rd par - white
4th pair - white
5th pair - white
6th pair - red
7th pair - red
8th pair - red
9th pair - black

When she draws the 9th time we notice that she has drawn a pair of each socks.

Since we always need to consider the worst case scenario, the answer would be 9