winnie has 7 trophies she wants to display in arrays. how many different arrays are possible? explain.
1because I said 1&7
There are 3 arrays
To determine the number of possible arrays Winnie can use to display her 7 trophies, we need to understand the concept of permutations.
In mathematics, a permutation is an arrangement of objects in a specific order. The formula to calculate permutations is given by nP r = n! / (n-r)!, where n represents the total number of objects, and r represents the number of objects selected.
In this case, Winnie wants to display her 7 trophies in arrays. Since the order of the trophies within each array matters, we need to use permutations.
Let's assume Winnie wants to display her trophies in groups of 3. We can calculate the number of possible arrays using the formula mentioned earlier: 7P3 = 7! / (7-3)! = 7! / 4! = (7 * 6 * 5 * 4!) / 4! = 7 * 6 * 5 = 210.
Therefore, Winnie can create 210 different arrays to display her 7 trophies if she arranges them in groups of 3. The number of arrays will vary depending on the group size she wants to display her trophies in.
To determine the number of different arrays possible for displaying Winnie's 7 trophies, we need to consider the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, the trophies are the objects that Winnie wants to display, and the order in which the trophies are arranged in the array is significant.
To calculate the number of different arrays, we can use the factorial function. The factorial of a number n, denoted by n!, is the product of all positive integers less than or equal to n.
In this case, we have 7 trophies to arrange in the array. So, the number of different arrays possible can be calculated as 7!.
To find the value of 7!, we multiply all positive integers less than or equal to 7: 7 × 6 × 5 × 4 × 3 × 2 × 1.
Calculating the value, we get: 7! = 5040.
Therefore, there are 5040 different arrays possible for displaying Winnie's 7 trophies.