A conference is to have eight presentations over the course

Question

A conference is to have eight presentations over the course of one day, consisting of three long presentations, and five short presentations. If the conference organizer doesn't want consecutive long presentations, and the conference is to start with a short presentation, how many schedules of presentations are possible?

A. 120
B. 720
C. 2880
D. 5760
E. 11520

the book says the answer is 2880 which I dont agree with.

I have the possible ways of 5short and 3long = 720.
then the possible arrangement = 7
so I got 5040.

To find the arrangement, i had to draw squares and fill then with the symbols of Ss and Ls.

Anyone knows better ways or equation for this?

Juz2play · Answer

There are altogether 10 arrangements though. The best approach is the slotting method like what you had done. From what I googled, this question has both wrong OA and OE. The answer should be 7200 (720*10). Placed L at slot 2, there would be 6 arrangements. Placed L at slot 3, there would be 3 arrangements. Lastly, placed L at slot 4, there would be 1 arrangement. We cannot placed L at slot 5 and onward because it would violate the question constraint. So, there are a total of 10 arrangements. Cheer!

Bunuel · Answer

S*S*S*S*S*

5 short presentations can be arranged in 5!=120 ways.

As for 3 long presentations: each can be placed instead of any of the 5 star, so in  C^3_5=10  ways, and they also can be arranged in 3!=6 ways.

Total = 120*10*6 = 7,200.

No correct answer among the options.

nitin6305 · Answer

Bunuel, can you give a solution with the opposite approach, total minus always together. I am not able to get the approach correctly.

Thanks

rango · Answer

Baffled with the pattern of Q. I find out following combinations; SLSLSLSS SSLSLSLS SSSLSLSL Can't find the way to solve the problem. :shock:

Bunuel · Answer

Notice that all S's and all L's there are different and re-read my post.

Hope it helps.

rango · Answer

You mean that you first find out the no. of ways S selection, then ways of L selection, then the ways of arrangements of S and L and atlas multiply all the ways to get the final answer.

Thanks Bunuel

A conference is to have eight presentations over the course

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