Factorial computations play a part in determining how many combinations of possible plant layouts need to be considered.How many combinations need to be studied with five work centers?
A)25
B)120
C)3125
D)60

Question

Quizplus · Accepted Answer

The number of combinations of possible plant layouts with five work centers can be found using the formula for permutations with repetition: n^r where n is the number of options for each position and r is the number of positions. In this case, there are 5 options for each position (since there are 5 work centers) and 5 positions. Therefore, the number of possible combinations is 5^5 = 3125. However, we are only concerned with unique combinations, so we use the formula for combinations: n!/(r!(n-r)!), where n is the total number of options (3125) and r is the number of options we choose at a time (5). This simplifies to 3125!/5!(3125-5)! = 3125!/5!3120! = 120, which is the number of unique combinations that need to be studied. Therefore, the best choice is B.

Factorial Computations Play a Part in Determining How Many Combinations