gmatchallenge
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- Oct 19, 2019
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While preparing for GMAT I came across one of the questions.
I have been able to apply concepts to 4 out of 5 sub questions but even after spending a day trying to look for similar questions and solutions I am stumped.
Q. A large box of biscuits contains nine different varieties. In how many ways can four biscuits be chosen if:
(1). all four are different.
A. So this one is pretty straight forward. We have to select 4 different types of biscuits so we have 9C4 or 124 ways.
(2). two are the same and the others different.
A. This was a tough one for me and even though I got the answer correct, I am not sure if my approach was correct. Switching to slot method : 9X1X8X7/2! = 252. 9X1 shows same selection for two positions where originally 9 options were available. 8x7 shows the possibilities for last 2 slots which have to be populated by different varieties. 2! accounts for double repetition among 8x7.
(3). two each of two varieties are selected.
A. I cant seem to make logic for this one. Going by the slot method I think it should be 9x1x8x1. However, looking at the answer there appear to be some repetitions that I haven't taken out. How can there be repetitions ?
Slot 1 : 9 options
Slot 2 : Same as slot 1
Slot 3 : 8 options
Slot 4 : Same as slot 3.
If there are repetitions here then why didn't we account for them in (2) among repeated and non-repeated elements. i.e in (2) there were repetitions among 8x7 only and not 9x8x7 i.e 3! - Why ?
(4). three are the same and the fourth different
A. 9x1x1x8 = 72 (Again, why are there no repetitions between repeated and non-repeated elements)
This question looked basic but this has challenged my understanding and concepts regarding P&C with repetitions.
Will appreciate your input.
I have been able to apply concepts to 4 out of 5 sub questions but even after spending a day trying to look for similar questions and solutions I am stumped.
Q. A large box of biscuits contains nine different varieties. In how many ways can four biscuits be chosen if:
(1). all four are different.
A. So this one is pretty straight forward. We have to select 4 different types of biscuits so we have 9C4 or 124 ways.
(2). two are the same and the others different.
A. This was a tough one for me and even though I got the answer correct, I am not sure if my approach was correct. Switching to slot method : 9X1X8X7/2! = 252. 9X1 shows same selection for two positions where originally 9 options were available. 8x7 shows the possibilities for last 2 slots which have to be populated by different varieties. 2! accounts for double repetition among 8x7.
(3). two each of two varieties are selected.
A. I cant seem to make logic for this one. Going by the slot method I think it should be 9x1x8x1. However, looking at the answer there appear to be some repetitions that I haven't taken out. How can there be repetitions ?
Slot 1 : 9 options
Slot 2 : Same as slot 1
Slot 3 : 8 options
Slot 4 : Same as slot 3.
If there are repetitions here then why didn't we account for them in (2) among repeated and non-repeated elements. i.e in (2) there were repetitions among 8x7 only and not 9x8x7 i.e 3! - Why ?
(4). three are the same and the fourth different
A. 9x1x1x8 = 72 (Again, why are there no repetitions between repeated and non-repeated elements)
This question looked basic but this has challenged my understanding and concepts regarding P&C with repetitions.
Will appreciate your input.