Counting Combos: 5 T-Shirts & 3 Jeans: 15 Days

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SUMMARY

The discussion centers on calculating the number of unique outfit combinations a student can wear using five different t-shirts and three pairs of jeans. The first calculation is straightforward: 5 t-shirts multiplied by 3 jeans equals 15 unique combinations. However, the second calculation, which requires not repeating the same t-shirt on consecutive days, is misunderstood by some participants. The correct approach involves a more complex combinatorial analysis, leading to fewer than 15 valid combinations when adhering to the consecutive wear restriction.

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A student has five different t-shirts and three pairs of jeans.

How many days can the student dress without repeating the combination of jeans & t-shirt?
How many days can the student dress without repeating the combination of jeans & t-shirt and without wearing the same t-shirt on two consecutive days?

I think the first question is pretty easy and I got it right... 5x3 = 15 days.

I'm not sure if I'm missing something for the second question, but I'm still getting 15 days. The student could just wear Jeans 1 with Shirts 1-5, then Jeans 2 with Shirts 1-5, and finally Jeans 3 with Shirts 1-5 right?
 
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Abc123Def said:
A student has five different t-shirts and three pairs of jeans.

How many days can the student dress without repeating the combination of jeans & t-shirt?
How many days can the student dress without repeating the combination of jeans & t-shirt and without wearing the same t-shirt on two consecutive days?

I think the first question is pretty easy and I got it right... 5x3 = 15 days.

I'm not sure if I'm missing something for the second question, but I'm still getting 15 days. The student could just wear Jeans 1 with Shirts 1-5, then Jeans 2 with Shirts 1-5, and finally Jeans 3 with Shirts 1-5 right?

I don't see anything wrong with that.
 

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