Sets and counting methods

[anteater85]

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If 7 clubs enter a ranking contest and there are four ranks to be awarded-1st,2nd, third and fourth. how many different arrangements of ranked clubs are there?

 

[Jman1984]

Is it 840?

 

[bennijai]

Order is important in this problem so we need to use: nPr = n!/[n-r]!

7P4 = 7!/[7-4]! = 7!/3! = 7x6x5x4x3x2x1/3x2x1 = 7x6x5x4 = 840

 

[anteater85]

Order is important in this problem so we need to use: nPr = n!/[n-r]!

7P4 = 7!/[7-4]! = 7!/3! = 7x6x5x4x3x2x1/3x2x1 = 7x6x5x4 = 840

that's the correct answer
but when do we know to use the n!/[n-r]! or n!/r![n-r]!

 

[yumi43]

n!/[n-r]! or n!/r![n-r]!

the first equation is when order matters. the second equation is for figuring out combinations, when order doesn't matter.

 

[anteater85]

n!/[n-r]! or n!/r![n-r]!

the first equation is when order matters. the second equation is for figuring out combinations, when order doesn't matter.

Oh ok thank you sooooo much....

 

[navneetdh]

If 7 clubs enter a ranking contest and there are four ranks to be awarded-1st,2nd, third and fourth. how many different arrangements of ranked clubs are there?

order matters here because say jack is 1st jim is second and jake is 3rd. Will it be the same thing is jake is 1st, jim is third and jack is second? No. Those will be totally different ranks.

So you can have more arrangements, order matters ===>Permutation

 

[anteater85]

order matters here because say jack is 1st jim is second and jake is 3rd. Will it be the same thing is jake is 1st, jim is third and jack is second? No. Those will be totally different ranks.

So you can have more arrangements, order matters ===>Permutation

what are the key words to know if the order is important. I guess for this question since they say 1st, 2nd.....

 

[jefff]

first i made 4 dashes since there are 4 spots

_ _ _ _

then since there were 7 clubs, the first ranking can have a max of 7 clubs in it

7 _ _ _

the next spot can only have 6 in it (since one of the 7 will be in the 1st ranking)

7 6 _ _

im sure you catch the drift now... ok so now we have

7 6 5 4

7 x 6 x 5 x 4 = 840

hope this helps!

 

[navneetdh]

what are the key words to know if the order is important. I guess for this question since they say 1st, 2nd.....

dont really go for key words here. I was doing that before and getting 50% problems wrong. You have to understand the problem

Example of when order matters: I have the letters A B C D

ok now i have to make 2 letter acronyms

so AB and BA count as 2 diff things. because order matters for acronyms.

But if they just said make groups of 2 letters. So A,B and B,A are the same group. order does not matter. They will be considered same thing either way you put them. This is combinations when order does not matter. Sometimes in these problems they may say that make groups of two without repeating or something.

I hope it helps.

But definitely dont rely only on key words.