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John wants to place marbles in carry bags in such a way that some of t

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Carcass
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John wants to place marbles in carry bags in such a way that some of t [#permalink] New post   10 Aug 2023, 08:24
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John wants to place marbles in carry bags in such a way that some of the bags can be left empty.


Quantity A
Quantity B
Number of ways 5 different marbles can be placed in two different bags
25


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


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A
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Shusuman
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Re: John wants to place marbles in carry bags in such a way that some of t [#permalink] New post   19 Aug 2023, 00:52
Kindly explain
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John wants to place marbles in carry bags in such a way that some of t [#permalink] New post   19 Aug 2023, 02:25
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OE


John wants to place marbles in carry bags and it is given that the bags can be empty too (Hence, all the marbles can go to 1 bag also.)

It is given that there are 5 different marbles and 2 different bags.

Whatever is to be assigned, let’s make dashes for that.

\(M_1, M_2, M_3, M_4, M_5.\)

Number of ways to fill each dash = 2

Number of ways to fill 1st and 2nd and 3rd and 4th and 5th dash \(= 2 × 2 × 2 × 2 × 2 = 32\)

Quantity A = 32

Quantity B = 25

Since, Quantity A is greater than Quantity B.

Ans. (A)
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Re: John wants to place marbles in carry bags in such a way that some of t [#permalink] New post   05 Sep 2023, 07:27
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Always remember to put n different things into a r different groups We use the formula R^n
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Re: John wants to place marbles in carry bags in such a way that some of t [#permalink] New post   06 Mar 2024, 07:35
Carcass wrote:
OE


John wants to place marbles in carry bags and it is given that the bags can be empty too
(Hence, all the marbles can go to 1 bag also.)
It is given that there are 5 different marbles and 2 different bags.
Whatever is to be assigned, let’s make dashes for that.
M1 M2 M3 M4 M5
Number of ways to fill each dash = 2
Number of ways to fill 1st and 2nd and 3rd and 4th and 5th dash
= 2 × 2 × 2 × 2 × 2 = 32
Quantity A = 32
Quantity B = 25
Since, Quantity A is greater than Quantity B.
Ans. (A)


The phrasing is unclear; if I have M1 M2 in B1, and M3 M4 M5 in B2, is that not equivalent to having M1 M2 in B2, and M3 M4 M5 in B1? Shouldn't the result be 32/2 = 16 ?
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Re: John wants to place marbles in carry bags in such a way that some of t [#permalink] New post   29 Sep 2024, 00:51
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Hi Carcass,

Shouldn't it be 6 ways?

0,5
5,0
1,4
4,1
2,3
3,2

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Re: John wants to place marbles in carry bags in such a way that some of t [#permalink] New post   29 Sep 2024, 03:01
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Yes you are correc

The question is worded properly in my view

We have to consider that one bag can be completely filled up and the other would be empty or a mix of both

1st arrangement is 5 (all in one) and 0 (the other empty.

Then the unfolding is what you pointed out above

4:2
3:2
2:3
1:4
0:5

Because we do have OR one way OR the other the result should be 64 for QA
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Re: John wants to place marbles in carry bags in such a way that some of t [#permalink] New post   15 Dec 2024, 01:01
Carcass wrote:
OE


John wants to place marbles in carry bags and it is given that the bags can be empty too (Hence, all the marbles can go to 1 bag also.)

It is given that there are 5 different marbles and 2 different bags.

Whatever is to be assigned, let’s make dashes for that.

\(M_1, M_2, M_3, M_4, M_5.\)

Number of ways to fill each dash = 2

Number of ways to fill 1st and 2nd and 3rd and 4th and 5th dash \(= 2 × 2 × 2 × 2 × 2 = 32\)

Quantity A = 32

Quantity B = 25

Since, Quantity A is greater than Quantity B.

Ans. (A)


wouldn't this be 32 + the cased where both bags are empty and one of the bags is empty? how would you compute it
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Re: John wants to place marbles in carry bags in such a way that some of t [#permalink]
15 Dec 2024, 01:01
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