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Aryaa03
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Practice Questions Chat 31 May 2024, 11:12
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You can try listing various combinations e g (4,0,0) can be arranged in 3 ways. (1,2,1) and so on.

One of the club members has given solution using that approach on the link i sent earlier.
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Practice Questions Chat 31 May 2024, 11:19
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I mean, there are 5 people in a line to be arranged.
So we fill 5 dashes acc to questions demand.
And here there is given 3 boxes and 4 balls.

Why not do the same here like 3 boxe’s dashes to be filled with 4 balls.
In the first box, 4 balls can go, in the second box, 4 and 4 in the third.
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Practice Questions Chat 31 May 2024, 21:57
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PrabhatKC
There are 3 boxes and 4 balls.
So How Come this is not 4^3?
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I counted 16 combinations

004 400 040 013 310 031 130 301 103 031 022 220 202 112 211 121. Can the be any more combinations
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Practice Questions Chat 31 May 2024, 22:16
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PrabhatKC
I mean, there are 5 people in a line to be arranged.
So we fill 5 dashes acc to questions demand.
And here there is given 3 boxes and 4 balls.

Why not do the same here like 3 boxe’s dashes to be filled with 4 balls.
In the first box, 4 balls can go, in the second box, 4 and 4 in the third.
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actually i also didnt read that part in the question says "box can have any number of marbles" mean box can contain zero as well

now choice is there with marble they have to select 3 boxes all so all marbles if possible can go in one box or divide them accordingly so there each marble has choice of selecting one of the box.

that is why 3^4
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Practice Questions Chat 31 May 2024, 22:21
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Lokster
004 400 040 013 310 031 130 301 103 031 022 220 202 112 211 121. Can the be any more combinations
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The counting is not so simple: every combination can have different selection of balls as balls are different. For example (1,0,3): first 3! ways in which 1, 0 and 3 balls can be placed. Next these 3 balls will have to be selected in 4C3 ways. So Box 1-1, Box 2-0 and Box3 -3 will not be one way but 4C3 ways as the 3 in box 3 can be selected in 4C3 ways. Thus, total ways for (1,0,3) will be 3!*4C3 or 24. SImilarly for others. They will add up to 81 or 3^4
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Practice Questions Chat 31 May 2024, 22:24
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Nullbyte
If the question was that each box needs to contain at least 1 marble, then would the answer been 4×3×2?
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@chetan2u, can you explain what happens in this case pls?
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chetan2u
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Practice Questions Chat 31 May 2024, 22:26
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Now, about 4^3 ways. This comes from any of the FOUR balls in boxes. Say balls are A, B , C and D, while boxes are X, Y and Z. For A in X, any of A, B, C, and D in Y and again any of A, B, C, and D in Z. But can the same ball A be there in all three boxes.....NO. But in case of 3^4, can same box X, have all four balls...YES. I hope it clears the query on why 3^4 and not 4^3.

Nullbyte
@chetan2u, can you explain what happens in this case pls?
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Nullbyte, that will not be correct. you are just filling three balls, what about the fourth one? Here, you will have to tak ethe possible combinations of boxes. It will be 1, 1, 2: Choosing the box with 2 balls can be in 3C1 or 3 ways. Next selecting/choosing 2 balls from 4 will be in 4C2 or 6 ways and then selecting one ball from the remaining two balls in 2C1 way and the remaining ball will go in the final box in 1C1 way.....3*4C2*2C1*1C1 = 3*6*2*1 = 36 ways.
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Practice Questions Chat 31 May 2024, 22:51
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chetan2u
Nullbyte, that will not be correct. you are just filling three balls, what about the fourth one? Here, you will have to tak ethe possible combinations of boxes. It will be 1, 1, 2: Choosing the box with 2 balls can be in 3C1 or 3 ways. Next selecting/choosing 2 balls from 4 will be in 4C2 or 6 ways and then selecting one ball from the remaining two balls in 2C1 way and the remaining ball will go in the final box in 1C1 way.....3*4C2*2C1*1C1 = 3*6*2*1 = 36 ways.
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Thanks for the explanation
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Practice Questions Chat 31 May 2024, 23:09
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chetan2u
The counting is not so simple: every combination can have different selection of balls as balls are different. For example (1,0,3): first 3! ways in which 1, 0 and 3 balls can be placed. Next these 3 balls will have to be selected in 4C3 ways. So Box 1-1, Box 2-0 and Box3 -3 will not be one way but 4C3 ways as the 3 in box 3 can be selected in 4C3 ways. Thus, total ways for (1,0,3) will be 3!*4C3 or 24. SImilarly for others. They will add up to 81 or 3^4
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Doubt: in case of 1,0,3 we have unique values. But what about 004 or 022? Can you count it the same way?
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Practice Questions Chat 01 Jun 2024, 00:32
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0,0,4: No unique values as all are in same box, but box can change in 3C1 ways, so 3 ways

022: Choose boxes in 3!/2! or 3 ways. Then choose 2 balls in 4C2 ways and the remaining 2 will automatically come out in 1 way, so 3*4C2*2C2 = 3*6*1 or 18 ways
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Practice Questions Chat 01 Jun 2024, 00:44
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Since I have written almost all ways for each combination, let me write the complete solution..
1,0,3: first 3! ways in which 1, 0 and 3 balls can be placed. Next these 3 balls will have to be selected in 4C3 ways. So Box 1-1, Box 2-0 and Box3 -3 will not be one way but 4C3 ways as the 3 in box 3 can be selected in 4C3 ways. Thus, total ways for (1,0,3) will be 3!*4C3 or 24.

1,1,2: Choosing the box with 2 balls can be in 3C1 or 3 ways. Next selecting/choosing 2 balls from 4 will be in 4C2 or 6 ways and then selecting one ball from the remaining two balls in 2C1 way and the remaining ball will go in the final box in 1C1, so .....3*4C2*2C1*1C1 = 3*6*2*1 = 36 ways
0,0,4: No unique values as all are in same box, but box can change in 3C1 ways, so 3 ways.
0,2,2: Choose boxes in 3!/2! or 3 ways. Then choose 2 balls in 4C2 ways and the remaining 2 will automatically come out in 1 way, so 3*4C2*2C2 = 3*6*1 or 18 ways.

Total: 24+36+3+18 = 81 ways or 3^4 ways
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Practice Questions Chat 01 Jun 2024, 01:33
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Guys how do you find units place of power has variables

Example 72^8p+2

Wrong group, apologies
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Practice Questions Chat 01 Jun 2024, 01:54
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8p means it i smultiple of 4. So, the unit sdigit will be same as that of 2^2 or it will be 4.
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Practice Questions Chat 01 Jun 2024, 02:24
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Just wanted to express gratitude for setting this up - it really helps when a certain daily question trips me up and reminds me of a forgotten concept. I'm sure this will eventually be helpful in my GMAT exam
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Practice Questions Chat 01 Jun 2024, 06:44
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Can someone please explain it
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Practice Questions Chat 01 Jun 2024, 07:25
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Kaushal124
Can someone please explain it
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Discussed in detail here: is-the-size-of-a-certain-particle-closer-to-10-3-centimeter-than-422862.html
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Practice Questions Chat 01 Jun 2024, 08:31
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relation cannot be determined because we dont know whether AB and DE are equal in length

Alex55,
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Practice Questions Chat 01 Jun 2024, 11:14
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hi guys, not a quant query but I have been facing an issue and don’t know how to solve it.
I have been prepping for the GMAT for a while now and I do fairly well while practicing. I am at the timed practice stage and can see myself getting better with the pacing but everytime I sit down to give a mock, my brain refuses to decode the logic in each question with passing time. Despite knowing the concepts and having a good accuracy, instead of trying to understand what the question is asking of me I immediately start recalling concepts and usually waste time by not getting to the exact strategy that the questions wants for me.

Any tips on how I can do better?
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Practice Questions Chat 01 Jun 2024, 11:15
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Then you need to go back to doing untimed with test like intensity, nothing over 3.5mins per question for now

Be easy with yourself, you know the math, don’t put too much pressure on you, also take a break for 2-3 days get away from the GMAT

and come back with a refreshed focus, exercise more, eat well, love life, the GMAT score will come

there are also more than one way to do the same question, so you are not wasting time, if the concept is good it should strike
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Practice Questions Chat 01 Jun 2024, 11:18
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Hey, thank you, As it turns out I have been taking too much pressure on acing the exam but my exam is on the 27th so I don’t think I can take days off
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