Official Quant thread for CAT 2013

MBA CAT 2024
13643
@getupsid said:
Q. the greatest possible number of points of intersection of 8 straight lines and 4 circles is a) 32b) 64c) 76d) 104
8 lines can intersct among each others in 8C2 ways, n 4 circles among each others in 2*4C2(coz it can intersect twice), n 4 circles n 8 lines may intrsct in 2*4c1*8c1 ways, so total
8C2+ 2*4C2+2*4c1*8c1=28+12+2*32=104
13644

find the no of ways in which 8 diffrnt flowers can be strung to form a garland when 4 particlar flowers are always 2gethr ??

13645
@shinoda said:
find the no of ways in which 8 diffrnt flowers can be strung to form a garland when 4 particlar flowers are always 2gethr ??
4!*4! ?

@shinoda -> @pyashraj has given a good explanation for the question you had asked buddy
13646
@pyashraj said:
@shinoda288 hoga shayad..
tht's what i think but the oa is 576..oa is wrong i guess..kyu?
13647
@shinoda said:
find the no of ways in which 8 diffrnt flowers can be strung to form a garland when 4 particlar flowers are always 2gethr ??
4!*4!/2. Divide by 2 as it is garland
13648
@Budokai001 said:
4!*4! ?
how come u came to this conclusion why not (4!/2)*(4!) ?
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@shinoda said:
find the no of ways in which 8 diffrnt flowers can be strung to form a garland when 4 particlar flowers are always 2gethr ??
cannot we treat 4 flowers as 1 entity, and then other 4 ...
so 4! the entities to arrange themselves, 4! for flowers to arrange in the single entity
so 4!*4! = 576
13650
@shinoda

Nahi nahi..OA is write..

The wrd "different" is used..nt same..Hence distinction hai..

Say suppose the question says..there are 8 people, 5 men n 3 women..Hw many ways 2 arrange them in circular fashion when all 3 women r always 2gether..Is ka answer 720 hoga..n nt 360..

We divide (n-1)! by 2 only when we cannot distinguish between anti-clockwise n clockwise arrangement..Jaise in the last ques of urs..

Thus, In this ques..It will be (5-1)!*4! = No. of ways of arranging the flowers*No. of arranging the flowers amongst themselves..

=>576 hi hoga... :)
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@shinoda said:
tht's what i think but the oa is 576..oa is wrong i guess..kyu?
4!*4! = 576... isn't oa ryt?
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@pratskool Bro should we divide it by 2 after the 4!*4! since we already considered circular permutations .. ?
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@Budokai001 said:
@pratskool Bro should we divide it by 2 after the 4!*4! since we already considered circular permutations .. ?
i did not divide it by 2 newere.. i guess u misread my solution... i said it should be 4!*4!
bro, when a garland is considered, it is placed infront of u, clockwise and anticlockwise looks different, hence we are not dividing by 2 .... divide by 2 when both clockwise and anticlockwise are alike
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@shinoda said:
find the no of ways in which 8 diffrnt flowers can be strung to form a garland when 4 particlar flowers are always 2gethr ??
4!*4!??
13655
@pyashraj said:
@shinodaNahi nahi..OA is write..The wrd "different" is used..nt same..Hence distinction hai..Say suppose the question says..there are 8 people, 5 men n 3 women..Hw many ways 2 arrange them in circular fashion when all 3 women r always 2gether..Is ka answer 720 hoga..n nt 360..We divide (n-1)! by 2 only when we cannot distinguish between anti-clockwise n clockwise arrangement..Jaise in the last ques of urs..Thus, In this ques..It will be (5-1)!*4! = No. of ways of arranging the flowers*No. of arranging the flowers amongst themselves..=>576 hi hoga...
so if we go by tht logic then in the qn given below (from the same book) they give the oa with a different approach.

find the no of ways in which 10 different beads can be arranged to form a necklace.

p.s.: i too got confused by the "different" word.
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@shinoda

Should be 9!/2..

Since 10 beads are arranged in a circle relative to themselves, so they can be arranged in (10-1)1 = 9!..In these 9! arrangements of beads clockwise n anti-clockwise arrangements cannot be distinguished..

Hence will be 9!/2..
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@shinoda

Solve this:

Hw many ways can 6 beads of different colors be arranged to form a necklace?
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@shinoda said:
so if we go by tht logic then in the qn given below (from the same book) they give the oa with a different approach.find the no of ways in which 10 different beads can be arranged to form a necklace.p.s.: i too got confused by the "different" word.
9!/2 ??
13659
@pyashraj said:
@shinodaShould be 9!/2..Since 10 beads are arranged in a circle relative to themselves, so they can be arranged in (10-1)1 = 9!..In these 9! arrangements of beads clockwise n anti-clockwise arrangements cannot be distinguished..Hence will be 9!/2

so it means tht those 4 alwys togehtr wala set made the whole change..and anticlockwise and clockwise arngment got changed ??
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@shinoda said:
so if we go by tht logic then in the qn given below (from the same book) they give the oa with a different approach.find the no of ways in which 10 different beads can be arranged to form a necklace.p.s.: i too got confused by the "different" word.
9!/2
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@pyashraj said:
@shinodaSolve this:Hw many ways can 6 beads of different colors be arranged to form a necklace?
won't this be same - 5!/2
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@shinoda said:
find the no of ways in which 8 diffrnt flowers can be strung to form a garland when 4 particlar flowers are always 2gethr ??
4! * 4!