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In how many different ways can a soccer team finish the season with th
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14 Oct 2021, 09:30
14 Oct 2021, 09:30
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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
(A) 6
(B) 20
(C) 60
(D) 120
(E) 240
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Re: In how many different ways can a soccer team finish the season with th
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14 Oct 2021, 10:05
14 Oct 2021, 10:05
1
Carcass 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
(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: C
Re: In how many different ways can a soccer team finish the season with th
[#permalink]
22 Jan 2022, 03:31
22 Jan 2022, 03:31
Why is the approach not = 3*2*1?
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: C
GreenlightTestPrep wrote:
Carcass 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
(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: C
