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

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In summary: So in summary, a student with five different t-shirts and three pairs of jeans can dress without repeating the combination of jeans and t-shirt for 15 days. And without wearing the same t-shirt on two consecutive days, they can still dress for 15 days by rotating through all the jeans and t-shirts.
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Abc123Def
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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.
 

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

How many possible combinations can be made with 5 t-shirts and 3 jeans over a period of 15 days?

There are 90 possible combinations that can be made with 5 t-shirts and 3 jeans over a period of 15 days. This can be calculated by multiplying the number of t-shirts (5) by the number of jeans (3) and then multiplying that by the number of days (15). So, 5 x 3 x 15 = 90.

Can a t-shirt or a pair of jeans be worn more than once in a 15-day period?

Yes, a t-shirt or a pair of jeans can be worn more than once in a 15-day period. The number of combinations only shows the number of unique outfit options, but it is possible to repeat outfits.

How many different outfits can be made with 5 t-shirts and 3 jeans?

There are 8 different outfits that can be made with 5 t-shirts and 3 jeans. This can be calculated by adding the number of t-shirts (5) to the number of jeans (3), so 5 + 3 = 8.

Can a t-shirt and a pair of jeans be worn together more than once in a 15-day period?

Yes, a t-shirt and a pair of jeans can be worn together more than once in a 15-day period. The number of combinations only shows the number of unique outfit options, but it is possible to repeat outfits.

How can the number of combinations change if there were 10 t-shirts instead of 5?

If there were 10 t-shirts instead of 5, the number of possible combinations would increase to 240. This can be calculated by multiplying the number of t-shirts (10) by the number of jeans (3) and then multiplying that by the number of days (15). So, 10 x 3 x 15 = 240.

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