Joey is planning to throw a small party...

LUANDATO wrote:Joey is planning to throw a small party and for that he needs to do the following tasks:

I. Decide guest list.
II. Send invites.
III. Arrange catering.
IV. Decide the venue.
V. Rent a music system.

The tasks can be done in any order as long as the invites are sent after the guest list is decided. In how many ways can Joey do the five tasks listed above?

A. 24
B. 48
C. 60
D. 120
E. 240

Alternate approach:

Let the 5 tasks = A, B, C, D and E.
To complete the tasks, Joey must create a schedule with 5 positions.
Since task A (deciding a guest list) must be completed before task B (sending invites), A must appear TO THE LEFT OF B in the schedule.

Number of options for C = 5. (Any of the 5 positions in the schedule.)
Number of options for D = 4. (Any of the 4 remaining positions in the schedule.)
Number of options for E = 3. (Any of the 3 remaining positions in the schedule.)
Number of options for A = 1. (Of the 2 remaining positions, the one more to the left must be occupied by A, since A must appear to the left of B in the schedule.)
Number of options for B = 1. (Only 1 position remains.)
To combine the options above, we multiply:
5*4*3*1*1 = 60.

The correct answer is C.