icemanKK wrote:Hi Brent,
I have come across logic that you posted in a lot of places but cant seem to figure it out properly.
I shall provide an example below. Can you please tell me if this scenario and it solution is comparable to the above problem.
Lets us say we have 3 letters and 2 places to put them in (similar to the problem above)
The number of ways the first place can be filled = 3
The number of ways the second place can be filled = 2 (problem is without replacement as in the case of the letters)
Total No. of ways = 6 but generally I find that these have solutions 3^2.
I cant seem to differentiate between the 2 types of problems (the one posted above and mine).
How many ways can 3 letters be placed into 2 boxes, if it is possible for all 3 letters to be placed into the same box?
EACH LETTER must choose a box because each letter must be placed inside one of the boxes.
But it is NOT necessary that EACH BOX choose a letter, since it's OK for a box to be empty.
Thus, we count the number of options from the viewpoint of EACH LETTER.
The number of options for the first letter = 2. (Either of the 2 boxes.)
The number of options for the second letter = 2. (Either of the 2 boxes.)
The number of options for the third letter = 2. (Either of the 2 boxes.)
To combine these options, we multiply:
2*2*2 = 2³ = 8.
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