Tony has 3 jackets and 2 shirts and 2 pants. He wants to wear three items every day. How many outfits he can choose of the same clues and/or of different clues
Is it compulsory to wear all 3 outfits?
yes
3c1*2c1*2c1=12
Can you please illustrate details? Thank you
To calculate the number of outfits Tony can choose, we need to determine the combinations of three items he can select from his collection of jackets, shirts, and pants.
First, let's consider outfits with the same clues (e.g., all jackets, all shirts, or all pants). Tony can choose three items from each category in the following ways:
1. Jackets: Since Tony has three jackets, he can choose any combination of three jackets. This can be calculated using the formula for combinations: C(n, r) = n! / (r! * (n - r)!), where n is the total number of items (3 jackets), and r is the number of items chosen (3). In this case, C(3, 3) = 3! / (3! * (3-3)!) = 1. So, Tony can choose 1 combination of three jackets.
2. Shirts: Similarly, since Tony has two shirts, he can choose any combination of two shirts. Using the combination formula, C(2, 2) = 2! / (2! * (2-2)!) = 1. So, Tony can choose 1 combination of two shirts.
3. Pants: Tony has two pants, and he needs to choose one. Using the combination formula, C(2, 1) = 2! / (1! * (2-1)!) = 2. So, Tony can choose 2 combinations of one pant each.
Next, let's consider outfits with different clues (e.g., a combination of jackets, shirts, and pants). We need to find the combinations of one item from each category. Using the combination formula:
Combination = (Number of choices for jackets) * (Number of choices for shirts) * (Number of choices for pants)
Combination = C(3, 1) * C(2, 1) * C(2, 1) = 3 * 2 * 2 = 12
So, Tony can choose 12 different combinations of outfits consisting of items from different categories.
To summarize, Tony can choose:
- 1 combination of three jackets
- 1 combination of two shirts
- 2 combinations of one pant each
- 12 combinations of items from different categories.