Question

There are twenty stores for a grocery chain in the Mid-Atlantic region. The regional executive wants to visit five of the twenty stores. She asks her assistant to choose five stores and arrange the visit schedule. (Show all work. Just the answer, without supporting work, will receive no credit). (a) Does the order matter in the scheduling? (b) Based on your answer to part (a), should you use permutation or combination to find the different schedules that the assistant may arrange? (c) How many different schedules can the assistant recommend?

Answer 1

(a) Does the order matter in the scheduling?

Yes, the order does matter in the scheduling, because scheduling will change if the order is change for selected grocery stores.

(b) Based on your answer to part (a), should you use permutation or combination to find the different schedules that the assistant may arrange?

Based on answer to part (a), you should use permutation to find the different schedules that the assistant may arrange. We know that order is important in permutation and order is not important in combination. For example, two observations A and B forms pairs AB and BA. In permutation AB and BA are different but they are same in combination.

(c) How many different schedules can the assistant recommend?

We are given n=20, x = 5

_nP_x = P_{(n, x)} = n!/(n – x)!

₂₀P₅ = P_{(20, 5)} = 20!/(20 – 5)! = 20!/15! = 20*19*18*17*16*15! / 15! = 20*19*18*17*16 = 1860480

Total number of possible schedules = 1860480