1.A furniture store sells couches that are available in 3 different styles, 7 different colors, and 2 different sizes. How many different couches are available?
- If I multiply all of these, would that give me the answer? If so, the answer would be 42.
2.In how many different ways can 6 students stand in a row of 6?
Thanks
-MC
1. correct.
2. 6*5*4*3*2*1=6!=you do it.
Thought so, thanks!
-MC
1. Oh wow, 42 options for couches? That's the meaning of life, the universe, and comfy seating all in one! But no, multiplying 3 styles, 7 colors, and 2 sizes won't give you the correct answer. You need to multiply the number of options for each category, which gives us 3 * 7 * 2 = 42 *styles, colors, sizes* in total!
2. Ah, arranging students in a row, the classic human dominos game! So, with 6 students and 6 spots, it's like having a row of empty chairs at a comedy club waiting for the punchline of the lineup. There are 6 factorial ways to arrange them, which is 6! (pronounced as 6 factorial). That's 6 x 5 x 4 x 3 x 2 x 1, and it equals 720 different ways those students can strut their stuff!
1. No, multiplying all the given options will not give the correct answer. To find the total number of different couches available, you need to multiply the number of options for each category.
In this case, there are 3 different styles, 7 different colors, and 2 different sizes. To find the total number of different couches, you need to multiply these numbers: 3 x 7 x 2 = 42.
So, the correct answer is 42.
2. If there are 6 students standing in a row, the number of different ways they can stand can be determined using the concept of permutations. The formula for permutations of n objects, taken r at a time, is given by nPr = n! / (n-r)!
In this case, there are 6 students, so n = 6. The students are standing in a row, so the order matters, and all 6 students will be standing in a row, so r = 6.
Using the formula, the number of different ways the 6 students can stand in a row would be calculated as follows:
6P6 = 6! / (6-6)! = 6! / 0! = 6! / 1 = 6 x 5 x 4 x 3 x 2 x 1 / 1 = 720 / 1 = 720
Therefore, there are 720 different ways the 6 students can stand in a row.
1. To calculate the number of different couches available, you need to use the concept of the multiplication principle, also known as the fundamental counting principle. The multiplication principle states that if there are m ways to do one thing and n ways to do another, then there are m*n ways to do both things.
In this case, since there are 3 different styles, 7 different colors, and 2 different sizes, you can multiply these numbers to get the total number of different couches available: 3 * 7 * 2 = 42. So, yes, your calculation is correct and there are indeed 42 different couches available.
2. To determine the number of different ways 6 students can stand in a row of 6, you need to use the concept of permutations. A permutation is an arrangement of objects in a specific order.
In this case, you have 6 students and 6 spots in the row. The first spot can be filled by any of the 6 students. Once the first spot is filled, there are 5 students remaining to fill the second spot. Similarly, there are 4 students remaining for the third spot, 3 students for the fourth spot, 2 students for the fifth spot, and the last student will fill the sixth spot.
To calculate the total number of permutations, you can multiply the number of options for each spot: 6 * 5 * 4 * 3 * 2 * 1 = 720.
So, there are 720 different ways the 6 students can stand in a row of 6.