Cher has forgotten the combination to her locker. She knows it consists of four numbers -- 3, 5, 7, and 9 -- but she can't recall the order. She decides to try every possible order until she gets the right one.
How many possible orders are there?
The Correct Answer is: 24 orders
Four possibilities for the first number.
Four possibilities for the second number
Therefore, 4x4 = 16 possibilities for the first two numbers.
Four possibilities for the third number
Therefore, 16x4 = 64 possibilitites for the first three numbers.
I think you can now see what the total number of arrangements of all four numbers will be.
6 orders
To determine the number of possible orders, we need to calculate the number of permutations of the four numbers -- 3, 5, 7, and 9.
We can use the formula for permutations, which is given by n! / (n - r)!, where n is the total number of items and r is the number of items taken at a time.
In this case, we have four numbers and we want to arrange all four of them, so n = 4 and r = 4. Plugging these values into the formula:
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24.
Therefore, there are 24 possible orders for Cher's locker combination.