In how many way can 5 boys and 6 girls be arranged in a row so that no two boys are together ?
A) (5!)(6!)
B) (6!)(7C5)
C) 7P5+(6!)
D) (7P5)(6!)
E) (5!)+(6!)
GRE Question of the Day: Permutation and Combination
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the answer is A)5!*6!
first arrange 5 boys with spaces btw them….5! ways
on either side of each boy a girl cn be seated….in 6!ways
hence the total num of possible comb are…
5!*6!ways.
he is assuming himself that 5!means boys are sitting with spaces between them
i think its b
hi dhaval,
what is your logic ?
is the question correct?….
my ans goes closer to B)…….but not exactly
Dear nutboltoo,
Why you think so ?
.1.2.3.4.5.6.
5 boys can be arranged in 7 spaces between the girls(shown by dots above) in 7c5 ways.6 girls can be arranged among themselves in 6! different ways.
therefore,total number of ways=7c5*6!
Now avinash your turn to explain your answers.
even i think A.
Dear Gurleen,
What is wrong in dhaval’s explanation ?
welll dhaval…uve gottu remember tht there are only 5 boys…n when u try to arrange them between girls ..where there are 7 places there is a possibility of two boys sitting side by side…( try placing 1 boy in the first place and other in the last place…ull know it)
in these type of probs u always gottu first fix the persons who r less in number…(its boys in this case…)n then give paces to others between them….
hope u got it ppl..im open to discuss furthur..:)
In these type of probs u always gottu first fix the persons who r less in number
>> What is basis of this argument ? I think it’s ur owm opinion.
Second Question:
Why you can not arrange like Dhaval did ?
ohhh sorry ppl ive completely misread the ques….newaysss…
intrestingly i strongly go wid option D)…..i know strange no1 ws wid tht answer..
dhaval ws close but he juss selected the places btw girls rather thn permuting…..
fix 6 places for girls n in the available 7 places 5 boys cn be inserted..(inter jumbling them.)
therefore…
………………..6!*7p5………………
(dhaval uve made the same mistake of juss selecting places in one of the prev. probs if my memery goes rite..)
hmmm gre taker its u finally whos gottu explain to us guyss…….its only u who knows the correct answer..
Great reply from the man who roaring for GRE 1600 !!!!!!!!
Avinash ultimately u got it.
correct answer is D.
Important Note:
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# Difficult GRE Questions
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In “Very Hard GRE Questions ” category we put those questions, in which most you of make silly mistakes. It would be helpful for revision in later days or before the Real GRE Test. If you like you can post some interesting facts or formula for those questions Or how you struggle to solve those qurestions.
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TakeGRE Team
D
d
B is d answer5
Dear sateesh_rahul,
correct answer is D. Pls read above comments specially avinash.
good Q. but i dont think this was a tough one. there r some permutation/comb Qs in which u need to find the prob of one event after another had occurred. those r the real tough ones
Dear Viren,
Thanks for your comment, We will be more than happy if you can share some of those questions at http://www.takegre.com/index.php/ask-a-gre-question/
Thanks in advamce.
TakeGRE Team.
hey i dont have them here now. but those Qs are like –
a coin was tossed three times. 1) whats the probablity of getting at least two tails. 2) whats the prob of getting at most two tails.
there are also some others in which they ask u to find the prob. of some event after one event has occurred.
Dear Viren,
Thanks for your concerned reply. We got your point.
We will try to add those questions as soon as possible.
Bye
TakeGRE Team
the answer is D.
6!*7c5
the correct ans is (d)
in the ques it is asked to make the arrangements so that no two boys sit together. for this purpose we will first arrange the girls. Now 6 girls can be arranged in 6! ways after arranging the 6 girls we have 7 places to arrange 5 boys in order to avoid any 2 being sit together. This means 5 boys can be arranged in 7 places in 7P5 ways
thus according to multiplication rule
total number of ways become 7P5(6!)
shilpa great explanation tnks….
my answer is b- 6!*7C5
b g b g b g b g b g b g b
6 girls = 6!
out of 7 possibility for boys 5 we have to select = 7C5
D
girls can be chosen in 6! ways and boys can be chosen in 5! ways , questions is very clear.