How to look feminine amid 3 macho men
One day, when Brenda's three brothers - Charles, Darius and Alfred - first got their motorbikes, she wanted to take a photo with her brothers starting their motorbikes.
Her brothers decided to line their three motorbikes in a certain row but she was considering whether to stand among the motorbikes or to ride pillion on one of them.
To look even more feminine, she narrowed down her attire to the following possibilities:
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2 sleeveless blouses
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2 crop T-shirts
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2 pairs of hot pants
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3 skirts
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4 dresses
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3 pairs of high heels
To enhance the effect, she also considered posing in the photo in one of the following ways:
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Puckering her pretty red lips
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Smiling with her teeth exposed
Finally, Brenda was also thinking of whether to do a piece sign in the photo.
How many different ways are there for Brenda to appear in the photo?
Details and assumptions
- Brenda's dresses cover her whole body. If she doesn't wear them, she needs clothing for both her upper and lower body to look decent.
- Brenda must have footwear.
The answer is 2016.
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1 solution
In terms of how she wants to appear among the three motorbikes, she can either stand among them or ride pillion on one of them. To stand among them, there are 4 positions for her (2 ends or 2 gaps between the 3 motorbikes). There are also of course 3 possibilities if she chooses to ride pillion on one of the three motorbikes. By addition principle, we have 4 + 3 = 7 ways here.
In terms of her attire, we consider if she wears two pieces. For her upper body, we have 4 possibilities (2 sleeveless blouses or 2 crop T-shirts) while for her lower body, we have 5 possibilities (2 pairs of hot pants and 3 skirts). Here we use multiplication principle instead so this gives us 4 ∗ 5 = 2 0 ways. Considering if she chooses to wear a dress, that's another 4 ways. So by addition principle, 2 0 + 4 = 2 4 ways. Also, she has 3 pairs of high heels to choose from. So by multiplication principle, 2 4 ∗ 3 = 7 2 ways.
In terms of her pose, she can either pucker her pretty red lips or smile with her teeth exposed so that's two ways. As for whether to do a piece sign, that's two ways again. Here we use multiplication principle again so we have 2 ∗ 2 = 4 ways.
In total, Brenda has 7 ∗ 7 2 ∗ 4 = 2 0 1 6 choices.