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the first colour which will have different colour in between can be selected in 7 ways
and remaining 6 colours can be selected and arranged in 6! ways
so total combinations are 7*6! >> 28
so Option A is correct
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What we have to do is choose a color for the wall, and then choose another color for the stripe.

For example, I can pick red for the wall and blue for the stripe. Conversely, I can pick the wall to be blue and the stripe to be red. Therefore, order matters when choosing the colors (it's not a combination question).

From here, just use the fundamental counting principle:

[Choose 1 of the 7 colors for the wall] * [Choose 1 of the remaining 6 colors for the stripe]
7*6 = 42.

This indicates that Quantity A is greater.


It's important to note why it's not a combination question. If I had decided to do (7 Choose 2), my result would've been 21, making B greater. But what is that actually mean?

If I were to use (7 Choose 2), what I would be doing is removing "duplicates". So in my example above with the colors blue and red, if I had chosen the color blue for the wall and red for the stripe, by selecting (7 Choose 2) as the method of computation, I've effectively removed the choice of the wall being red and the stripe being blue. We need to count those, so combinations is not the way to go.

To further illustrate: If I have a group of 7 people and I want to choose two for a committee, it would make sense to remove the duplicates. Picking, for example, John and Joe is the same as picking Joe or John. If however, one was to be President and the other Vice President, then picking John to president and Joe to be Vice President is not the same as John being Vice President and Joe being President.

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