haardiksharma wrote:
In how many different ways can a soccer team finish the season with three wins, two losses, and one draw?
(A) 6
(B) 20
(C) 60
(D) 120
(E) 240
Question rephrased: In how many different ways can we arrange the letters WWWLLD
-------------ASIDE--------------------------------------
When we want to arrange a group of items in which some of the items are identical, we can use something called the
MISSISSIPPI rule. It goes like this:
If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....] So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are
11 letters in TOTAL
There are
4 identical I's
There are
4 identical S's
There are
2 identical P's
So, the total number of possible arrangements =
11!/[(
4!)(
4!)(
2!)]
-------------NOW ONTO THE QUESTION!!--------------------------------------
WWWLLD
There are
6 letters in TOTAL
There are
3 identical W's
There are
2 identical L's
So, the total number of possible arrangements =
6!/[(
3!)(
2!)
= 60
Answer:
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