Latest TCS Aptitude Question SOLUTION: 15 students join a summer course. Every day 3 students are on duty after school to clean the class rooms. After the course, it was found that every pair of students has been on dut

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(#M40010796) TCS Numerical Ability question Keep an EYE

15 students join a summer course. Every day 3 students are on duty after school to clean the class rooms. After the course, it was found that every pair of students has been on duty exactly once. How many days does the course last for?
a) 35 b) 45 c) 105 d)none of these

Asked In TCS krishnamurthy (11 years ago)

Unsolved Read Solution (15)

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Read Solution (15) :

SDeep Bhattacharya  (11 years ago)

It is given in the prob., that every pair of students has been on duty exactly once. This suggests that the number of days the course lasts for is equal to the number of ways in which 2 students from 15 students can be selected.
Now, it is well-known fact that the number of ways in which 2 students from 15 students can be selected = (15C2) = [15!/{(13!)*(2!)}] = 7*15 = 105.

So, evidently, the course lasts for 105 days .

So, the correct answer is OPTION c) 105 .

Thanks to All..:-):-)

Is this solution Helpfull? Yes (50) | No (20)  

P M Anoop Sabir  (11 years ago)

no of pairs=15C2=15!/(2!13!)=7*15
no of pairs cleaning each day=3C2=3
no of days=7*15/3=35

Is this solution Helpfull? Yes (39) | No (8)  

PARAG KAMRA  (11 years ago)

sorry it will be
15c2=105(ans)

Is this solution Helpfull? Yes (13) | No (11)  

bhavatarini  (11 years ago)

HYE ITS GIVEN THAT E STUDENTS ARE ON DUTY..... HOW U GUYS TOOK 15C2???? its 15C3 naaaaa????

Is this solution Helpfull? Yes (12) | No (11)  

rutvee shah  (11 years ago)

@sdeep bhattacharya..the idea of taking 2 students at a time is correct..bt the q says 3 students form a pair...so the no days the course shud last shud be equal to the no of ways in which 3 students can b selectd out of 15 i.e. 15C3..

Is this solution Helpfull? Yes (10) | No (3)  

ankitbalyan  (11 years ago)

dekho bhai garmi ki chuttiya 45 din ki hoti hai to ans will be 45

Is this solution Helpfull? Yes (10) | No (10)  

Sankalp  (11 years ago)

the answer to this que. is a) 35, since total 105 pairs are present (14+13+12+11+..........+1=105) and each day 3 pairs are present (since 3 students form 3 pairs) hence 105 pairs will be present in 105/3 Days= 35 DAYs

Is this solution Helpfull? Yes (7) | No   

Navjyot Yadav  (11 years ago)

solution is not clear, all r wrong.
ans would be "none of these".

Is this solution Helpfull? Yes (6) | No (1)  

Navjyot Yadav  (11 years ago)

ans would be 15c2=105.
bcoz there will be only 105 pairs will appear for work exactly once.
logic is that remaing one out of three may be any student.
so two student r selected from combination of 15c2 at a time.

Is this solution Helpfull? Yes (4) | No (2)  

Chandra Sekhar  (11 years ago)

well,,i think it will be the combination of 15 students taking 2 at a time...
15C2=105
c)105

Is this solution Helpfull? Yes (3) | No (7)  

RAVI KIRAN  (11 years ago)

@P M ANOOP SABIR
your answer seems to be correct but y not the answer is 105

Is this solution Helpfull? Yes (3) | No (1)  

PARAG KAMRA  (11 years ago)

15+12+9+6+3=45
b)45(ans)

Is this solution Helpfull? Yes (2) | No (24)  

RAVI KIRAN  (11 years ago)

your answer seems to be correct but y not the answer is 105

Is this solution Helpfull? Yes (2) | No (2)  

shubham pal  (9 years ago)

it says three students not 2.......so the ans shd be 15c3
i.e. none of these d)

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palak  (9 years ago)

correct ans : 35
15C2 =105

and a group of 3 persons consists of 3 pairs

so 105/3=35

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