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A school teacher wants to divide the whole class into 3 groups with...

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A school teacher wants to divide the whole class into 3 groups with...  [#permalink]

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New post 21 Dec 2016, 04:38
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A school teacher wants to divide the whole class into 3 groups with an equal number of students in each group. The total number of students in her class is 24. Find out in how many ways can this be done?


A. \(^{24}C_8\)

B. \(\frac{^{24}C_8 * ^{16}C_8 * ^8C_8}{3!}\)

C. \(\frac{^{24}C_8 * ^{16}C_8 * ^8C_8}{3}\)

D. \(^{24}C_8 * ^{16}C_8 * ^8C_8\)

E. \(^{24}C_8 * ^{16}C_8 * ^8C_8\)\(* 3!\)


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Re: A school teacher wants to divide the whole class into 3 groups with...  [#permalink]

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New post 21 Dec 2016, 04:51
\(\frac{24!}{(8!)^3 * 3!} = \frac{_{24}C_8*_{16}C_8*_8C_8}{3!}\)

Answer B
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Re: A school teacher wants to divide the whole class into 3 groups with...  [#permalink]

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New post 21 Dec 2016, 04:59
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\(\frac{24!}{(8!)^3 * 3!} = \frac{_{24}C_8*_{16}C_8*_8C_8}{3!}\)

Answer B

That seems to be an identical question
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Re: A school teacher wants to divide the whole class into 3 groups with...  [#permalink]

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New post 21 Dec 2016, 17:03
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EgmatQuantExpert wrote:
A school teacher wants to divide the whole class into 3 groups with an equal number of students in each group. The total number of students in her class is 24. Find out in how many ways can this be done?


A. \(^{24}C_8\)

B. \(\frac{^{24}C_8 * ^{16}C_8 * ^8C_8}{3!}\)

C. \(\frac{^{24}C_8 * ^{16}C_8 * ^8C_8}{3}\)

D. \(^{24}C_8 * ^{16}C_8 * ^8C_8\)

E. \(^{24}C_8 * ^{16}C_8 * ^8C_8\)\(* 3!\)

Thanks,
Saquib
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Hi

The most important thing here :- all groups are identical

In 3 equal groups means 24/3 that is 8 in each group..
Choose 8 from total 24C8..
Choose 8 from remaining 16C8..
And finally remaining 8 are choosen 8C8

Total ways = 24C8 * 16C8 * 8C8..
But since the groups are identical ans these three groups can be arranged in 3!, Divide the ways by 3!

Ans B
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Re: A school teacher wants to divide the whole class into 3 groups with...  [#permalink]

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New post 08 Jun 2017, 00:30
chetan2u

Hi Chetan2u,

We are referring the groups identical because the no. of students are same?
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Re: A school teacher wants to divide the whole class into 3 groups with...  [#permalink]

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New post 08 Jun 2017, 05:52
Nitish7 wrote:
chetan2u

Hi Chetan2u,

We are referring the groups identical because the no. of students are same?



YES NITISH..

since the groups have same number and there is no other difference, these groups are identical..

example ..
there are three bags- same colour and same size- all bags are identical..
but say the bags are different in colour. not identical.. we will not divide by 31 or so
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: A school teacher wants to divide the whole class into 3 groups with...  [#permalink]

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New post 08 Jun 2017, 16:17
Hi,
I understood till you came up to 24C8*16C8*8C8.. But, I don't know why are dividing by 3!.
We don't need to arrange the 3 groups right?, we just want to find how many ways to get 3 groups.
Lets take A,B,C are 3 groups.
We don't want to find ABC, ACB,CAB etc..

Clearly I am not following you. Can you please explain me

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Re: A school teacher wants to divide the whole class into 3 groups with...  [#permalink]

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New post 28 Dec 2018, 11:30
chetan2u
I don't understand why the groups are identical.The students are not identical so how can the groups be identical?
In such questions do we have to presume the groups as same identity and ignore the diversity of students?
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Re: A school teacher wants to divide the whole class into 3 groups with...  [#permalink]

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New post 28 Dec 2018, 18:40
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arpitkansal wrote:
chetan2u
I don't understand why the groups are identical.The students are not identical so how can the groups be identical?
In such questions do we have to presume the groups as same identity and ignore the diversity of students?


Hi..
The reason is that we have not named the group..
So if A,B are in group I, C,D are in group 2 and E,F are in group 3..
It will be same when A,B are in group I, C,D are in group 3 and E,F are in group 2..
OR if A,B are in group 2, C,D are in group 1, and E,F are in group 3..

Since here all groups name and size wise are identical, all above distribution are identical, and hence we divide by 3!
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: A school teacher wants to divide the whole class into 3 groups with... &nbs [#permalink] 28 Dec 2018, 18:40
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