A mall has 5 gates. How many ways can one enter and exit at the mall
5 ways to enter
for each entry, 5 ways to exit
so, 5*5 = 25
To calculate the number of ways one can enter and exit the mall, we need to consider that there are multiple ordering possibilities.
Since you can enter and exit using different gates, we can consider the ordering of gate entries and exits separately. We can use the concept of permutations to calculate the number of ways.
Let's assume the 5 gates are labeled as gate A, B, C, D, and E.
For entering the mall:
- There are 5 options for the first gate choice.
- Since the gate choices can't be repeated, there are 4 options for the second gate choice.
- This pattern continues until the last gate, where there will only be 1 option left.
So, the number of ways to enter the mall is 5 * 4 * 3 * 2 * 1 = 120 ways.
For exiting the mall:
- Using the same logic, there are also 5 options for the first gate choice while exiting.
- Similarly, there will be 4 options for the second gate choice, 3 options for the third, 2 options for the fourth, and 1 option for the last.
So, the number of ways to exit the mall is also 5 * 4 * 3 * 2 * 1 = 120 ways.
To find the total number of ways to enter and exit the mall, we can multiply the number of ways to enter by the number of ways to exit:
Total number of ways = Number of ways to enter * Number of ways to exit = 120 * 120 = 14,400 ways.
Therefore, there are 14,400 different ways to enter and exit at the mall using the 5 gates.
To determine the number of ways one can enter and exit a mall with 5 gates, we can use the concept of combinations.
When entering and exiting the mall, we have two options for each action - enter or exit - at each gate. Therefore, we have 2 choices for each of the 5 gates, resulting in a total of 2 * 2 * 2 * 2 * 2 = 32 different possible combinations.
So, there are 32 ways one can enter and exit at the mall with 5 gates.