It is time to go shopping for new clothes for school! You have found
a catalog for new clothes. You decide that you will buy �ve di�erent
shirts, four di�erent pants, two di�erent jackets, and three di�erent
shorts. The catalog has twelve di�erent types of shirts, ten di�erent
types of pants, �ve styles of jacket, and �ve di�ernt shorts. In how
many ways can you order your new clothes from this catalog?
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To solve this problem, we need to use the concept of combinations.
To determine the number of ways to order your new clothes, we can multiply the number of choices for each category together.
1. Start with the shirts: Since you want to buy five different shirts out of twelve options, we can calculate this using the formula for combinations:
C(n, r) = n! / (r!(n-r)!)
C(12, 5) = 12! / (5!(12-5)!) = 12! / (5! * 7!) = 792
Therefore, you have 792 different ways to choose five shirts.
2. Move on to the pants: Out of ten different pants, you want to buy four, so we calculate:
C(10, 4) = 10! / (4!(10-4)!) = 10! / (4! * 6!) = 210
There are 210 different ways to choose four pants.
3. Next, consider the jackets: You want to buy two different jackets out of five styles. Again, using combinations:
C(5, 2) = 5! / (2!(5-2)!) = 5! / (2! * 3!) = 10
There are 10 different ways to choose two jackets.
4. Finally, we have the shorts: Out of five different shorts, you want to buy three, so we calculate:
C(5, 3) = 5! / (3!(5-3)!) = 5! / (3! * 2!) = 10
There are 10 different ways to choose three shorts.
To find the total number of ways to order your new clothes, we multiply the number of choices for each category together:
792 * 210 * 10 * 10 = 1,668,000
Therefore, there are 1,668,000 different ways to order your new clothes from this catalog.