Ask AI: You have two objects. If you add one more object, how many more permutations will there be?

To determine how many more permutations you will have when you add one more object, we need to look at the concept of permutations and factorials. The number of permutations of \( n \) objects is given by \( n! \) (n factorial), which is the product of all positive integers up to \( n \). - For 2 objects, there are \( 2! \) permutations: \[ 2! = 2 \times 1 = 2 \] - If you add one more object (making it 3 objects), then there are \( 3! \) permutations: \[ 3! = 3 \times 2 \times 1 = 6 \] To find out how many more permutations there are with 3 objects compared to 2 objects, subtract the number of permutations of 2 objects from the number of permutations of 3 objects: \[ 3! - 2! = 6 - 2 = 4 \] So, adding one more object increases the number of permutations by 4.

With two objects, you have 2! (2 factorial) permutations, which is 2*1 = 2 permutations. When you add one more object, you then have 3 objects, which means you have 3! (3 factorial) permutations, which is 3*2*1 = 6 permutations. So by adding one more object, you increased the number of permutations by 6 - 2 = 4 more permutations.