Final answer:
To determine the number of ways to display 4 certificates out of 7 when order matters, we calculate the permutation 7P4, which is 7! divided by (7-4)!. The result is 840 different choices.
Step-by-step explanation:
Since the order of the certificates does matter, the scenario described is a permutation problem, not a combination. To determine how many choices you have for displaying 4 certificates out of 7, we calculate the number of permutations for 4 items from a set of 7, which is usually denoted as 7P4. The formula for a permutation is nPr = n! / (n-r)!, where n is the total number of items to choose from, r is the number of items to choose, n! represents the factorial of n, and (n-r)! is the factorial of the difference between n and r.
Steps to calculate the permutation 7P4:
First, we would calculate the factorial of 7, represented as 7! (7 factorial), which is 7 x 6 x 5 x 4 x 3 x 2 x 1.
Next, calculate the factorial of the difference between the total items and the number of items to choose, which is (7-4)!. So, we calculate 3!, which is 3 x 2 x 1.
To illustrate, 7! equals to 5040, and 3! equals to 6. Dividing 5040 by 6 gives us 840.
Hence, you have 840 different choices for displaying 4 certificates out of 7 on the wall in a specific order.
Practicing by writing out all possible combinations for smaller numbers is a worthy exercise to understand the permutation concept.