Question

imagine you have a drawer with 5 different pairs of socks:

• 1 pair of red socks
• 1 pair of white socks
• 2 pairs of black socks with red stripes
• 1 pair of white socks with red stripes

you also have 3 different hats:

• a black hat with a red \b\ on the front
• a red-and-white hat for your favorite soccer team
• a solid blue beanie with a black bobble on top

sort the described combinations of socks and hats in order by the greatest number of possible options to the least.
start order
your outfit contains no red items.
your outfit contains only items with red.
all items in your outfit are partly black.
your outfit contains no black items.
end order

Explanation:

Step1: Analyze each combination

First, we determine the number of sock and hat options for each combination:

1. "Your outfit contains no red items"

- Socks without red: white (1 pair), black with red stripes? Wait, no—black with red stripes has red, so exclude. Wait, original socks: red (1), white (1), black with red stripes (2), white with red stripes (1). So socks without red: white (1) and... wait, black with red stripes has red, white with red stripes has red. Wait, no: the white socks (1 pair) and are there any others? Wait, the black socks with red stripes have red stripes, so they have red. The white with red stripes have red. So socks without red: white (1 pair) and... wait, the problem says "5 different pairs of socks": 1 red, 1 white, 2 black with red stripes, 1 white with red stripes. So socks without red: white (1) and... no, the black with red stripes have red, white with red stripes have red. So only white (1 pair) and... wait, no, the black socks with red stripes: do they have red? Yes, red stripes. So socks without red: white (1 pair) and... wait, maybe I miscounted. Wait, the pairs: red (1), white (1), black with red stripes (2), white with red stripes (1). So total pairs: 1+1+2+1=5. So socks without red: white (1) and... the black with red stripes have red, white with red stripes have red. So only white (1 pair) and... wait, no, the white socks are 1 pair, and are there any black socks without red? No, the black ones have red stripes. So socks without red: 1 (white) pair? Wait, no, the white socks are 1 pair, and the black with red stripes are 2 pairs (but they have red), white with red stripes 1 (has red), red 1 (has red). So socks without red: 1 pair (white). Wait, no, maybe the "black socks with red stripes"—do they count as having red? Yes, because red stripes. So socks without red: white (1 pair). Now hats without red: the solid blue beanie (1 hat), because the black hat has red "B", red-and-white has red. So hats without red: 1. So number of combinations: 1 (socks) * 1 (hats) = 1? Wait, no, maybe I made a mistake. Wait, let's re-express:

Socks:
- Red: 1 pair (has red)
- White: 1 pair (no red)
- Black with red stripes: 2 pairs (has red)
- White with red stripes: 1 pair (has red)

So socks without red: 1 pair (white).

Hats:
- Black with red "B": has red
- Red-and-white: has red
- Solid blue beanie: no red

So hats without red: 1 (blue beanie).

So combinations for "no red items": 1 (socks) * 1 (hats) = 1? Wait, that can't be right. Wait, maybe I messed up the socks. Wait, the "black socks with red stripes"—are they considered to have red? The problem says "contains no red items", so any item with red (even stripes) is excluded. So socks: red (has red), white (no red), black with red stripes (has red), white with red stripes (has red). So socks without red: 1 (white) pair. Hats without red: 1 (blue beanie). So 1*1=1.

2. "Your outfit contains only items with red"

Socks with red: red (1), black with red stripes (2), white with red stripes (1). So total socks with red: 1+2+1=4 pairs. Hats with red: black with red "B" (1), red-and-white (1). So hats with red: 2. So combinations: 4 * 2 = 8.

3. "All items in your outfit are partly black"

Socks partly black: black with red stripes (2 pairs) (black socks with red stripes—so partly black). Hats partly black: black with red "B" (black hat), solid blue beanie with black bobble (black bobble). So hats: black hat (1), blue beanie (1). So socks: 2 pairs (black with red stripes). Hats: 2 (black hat, blue beanie). So combinations: 2 * 2 = 4.

4. "Your outfit contains no black items"

Socks without black: red (1), white (1), white with red stripes (1). So socks: red (1), white (1), white with red stripes (1) → total 3 pairs. Hats without black: red-and-white (1, no black), solid blue beanie (no black? Wait, blue beanie has black bobble—so black. So hats without black: red-and-white (1). So socks: 3 pairs, hats: 1. Combinations: 3 * 1 = 3.

Wait, now let's recheck:

- "No red items": socks without red (white:1) * hats without red (blue:1) → 1*1=1
- "Only red items": socks with red (red:1, black with red:2, white with red:1 → 4) * hats with red (black with B:1, red-white:1 → 2) → 4*2=8
- "Partly black": socks with black (black with red:2) * hats with black (black hat:1, blue beanie with black bobble:1 → 2) → 2*2=4
- "No black items": socks without black (red:1, white:1, white with red:1 → 3) * hats without black (red-white:1, because blue beanie has black bobble → black, so exclude. So hats without black: red-white (1)) → 3*1=3

Now order from greatest to least:

"Only red items" (8) > "All partly black" (4) > "No black items" (3) > "No red items" (1)

Wait, but let's re-express:

Wait, "No black items": socks without black—red (1), white (1), white with red stripes (1) → 3 pairs. Hats without black: red-and-white (1, no black), blue beanie has black bobble (black), so hats without black: 1 (red-and-white). So 3*1=3.

"All partly black": socks with black—black with red stripes (2 pairs). Hats with black—black hat (1), blue beanie with black bobble (1) → 2 hats. So 2*2=4.

"Only red items": socks with red—red (1), black with red (2), white with red (1) → 4 pairs. Hats with red—black with B (1), red-white (1) → 2 hats. 4*2=8.

"No red items": socks without red—white (1 pair). Hats without red—blue beanie (1). 1*1=1.

So the order from greatest to least is:

1. Your outfit contains only items with red (8)
2. All items in your outfit are partly black (4)
3. Your outfit contains no black items (3)
4. Your outfit contains no red items (1)

Now, let's confirm each:

- "Only red items": 4 socks * 2 hats = 8
- "All partly black": 2 socks * 2 hats = 4
- "No black items": 3 socks * 1 hat = 3
- "No red items": 1 sock * 1 hat = 1

So the order is:

1. Your outfit contains only items with red
2. All items in your outfit are partly black
3. Your outfit contains no black items
4. Your outfit contains no red items

Answer:

1. Your outfit contains only items with red
2. All items in your outfit are partly black
3. Your outfit contains no black items
4. Your outfit contains no red items