Adam is making 4-layer dip for a party and has 6 ingredients from which to choose. In how many ways can he pick out and layer 4 ingredients?

This problem can be solved using the concept of permutations in combinatorics.

Step 1: Understand the problem Adam has 6 ingredients and he wants to make a 4-layer dip. This means he needs to choose 4 ingredients out of 6 and also decide the order in which to layer them.

Step 2: Apply the formula for permutations The formula for permutations is nPr = n! / (n - r)!, where n is the total number of options, r is the number of options to choose, and "!" denotes factorial.

Step 3: Substitute the given values into the formula In this case, n = 6 (the total number of ingredients) and r = 4 (the number of layers in the dip). So, the calculation becomes 6P4 = 6! / (6 - 4)!.

Step 4: Calculate the factorial values 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720 (6 - 4)! = 2! = 2 * 1 = 2

Step 5: Substitute the factorial values back into the formula 6P4 = 720 / 2 = 360

So, Adam can make his 4-layer dip in 360 different ways.