How many ways can 4 people be seated in a row of 6 chairs? (2021)

How many ways can 4 people be seated in a row of 6 chairs? (2021)

Step 1: Understand that we have 6 chairs and we want to seat 4 people in them.
Step 2: Realize that the order in which the people are seated matters. This means we are looking for permutations, not combinations.
Step 3: Use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of items (chairs) and r is the number of items to choose (people).
Step 4: In this case, n = 6 (chairs) and r = 4 (people). So we need to calculate 6P4.
Step 5: Plug the values into the formula: 6P4 = 6! / (6 - 4)! = 6! / 2!.
Step 6: Calculate 6! (which is 6 x 5 x 4 x 3 x 2 x 1 = 720) and 2! (which is 2 x 1 = 2).
Step 7: Now divide 720 by 2 to get 360.
Step 8: Conclude that there are 360 different ways to seat 4 people in 6 chairs.

Permutations – The arrangement of a subset of items from a larger set, where the order matters.
Factorial – The product of all positive integers up to a given number, used in calculating permutations.