2014-06-27 09:00:14

€  ™  ¶   ∫   fl

If the five symbols above are placed in a row so that € cannot be in the middle spot, how many different arrangements are possible?

The correct answer is 96
Explanation: Imagine that there are five spots available, like this:

__  __  __  __  __

Now, think of the number of symbols that can go in each slot. Start with the middle slot, since that cannot have the € symbol in it. Thus, there would be only 4 symbols that could be placed there, out of 5:

__  __  4  __  __

Now, for the first slot, there are 4 symbols left to choose from, the three that weren't placed in the center spot plus the added € symbol, which is allowed to go in that slot.  There would be 3 available for the next slot, 2 for the one after that, and 1 for the last slot (The symbol not yet used in the other slots):

_4_   _3_  _4_  _2_  _1_

Multiply these together to find the total number of arrangements available: 4 x 3 x 4 x 2 x 1 = 96