Latest TCS Aptitude Question SOLUTION: if there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?

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if there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?

Asked In TCS srivatsa (11 years ago)

Unsolved Read Solution (17)

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Read Solution (17) :

neha sharma  (11 years ago)

we have 5 sub and 6 periods so their arrangement is 6P5 and now we have 1 period which we can fill with any of the 5 subjects so 5C1
6P5*5C1=3600

Is this solution Helpfull? Yes (70) | No (11)  

himanshu umrao  (11 years ago)

5!*5*6=3600 ans
5 period full by=5!
remaining 1 period filled by=5
and this process occur =6 times

Is this solution Helpfull? Yes (30) | No (9)  

Amish Choudhary  (11 years ago)

Let us assume that we have 5 subjects named: M,E,H,P,C. Now arranging these so that each subject is allowed at least one period. M E H P C these five are arranged in 5! ways i.e. 120. NOW each time we have to arrange these 120 combination with each subject:-> - - - - - M,- - - - - E,- - - - - H,- - - - - P,- - - - - P, - - - - - C.These - blank places have 120 combination i.e. 1st with M, 2nd with M.........120th with M, Similarly these arrangements with E,H,P,C. So total 120+120+120+120+120 = 600.

Is this solution Helpfull? Yes (8) | No (22)  

Gaurab Kumar Das  (11 years ago)

THERE are 5 subjects we can arrange them by 6!/2!=1800
because 2 subjects are same at each day

Is this solution Helpfull? Yes (8) | No (6)  

Kalyan Y. Karbhar  (11 years ago)

six period can be arrange for 5 subject is P(6,5)
p(6,5)=720
remaning 1 period can be arrange using 5 subject is 5 ways
hence total number of way is 720*5=3600

Is this solution Helpfull? Yes (5) | No (3)  

dola  (11 years ago)

in a day 600 arrangements are possible
as 1st period = 5 ways,2nd= 5 ways, 3rd= 4 ways, 4th= 3 ways, 5th= 2 ways, 6th= 1 way,.....now 5*5*4*3*2*1= 600

Is this solution Helpfull? Yes (5) | No (5)  

Debanu Das  (11 years ago)

6P5*5C1=3600

Is this solution Helpfull? Yes (3) | No (6)  

Priyabrat Padhy  (11 years ago)

Which answer is true
?????

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

Shivendra Bhardwaj  (11 years ago)

5 to power 6
since 1st if 1st period is hindi next 5 period can be any1..then _5*5*5*5
for 5 subject = 5(_5*5*5*5) = 15625

Is this solution Helpfull? Yes (1) | No (16)  

Ankur Lakhani  (11 years ago)

6C5*5C1=30...is it correct?

Is this solution Helpfull? Yes (1) | No (13)  

Manan Saxena  (11 years ago)

each subject should be allowed at least one period thus 5 subjects can be arranged in 5! manner and the last period has 5 options thus.......answer will be 5!*5=600

Is this solution Helpfull? Yes (1) | No (5)  

guru  (9 years ago)

There are 6 periods and 5 subjects and these 5 subjects can be arranged in 6P5 =720 ways. The remaining period can be filled in 5 ways selecting any one of the subjects. But in each of the arrangement one subject is repeated, so we get a replica for each arrangement. So we need to divide the final answer by 2.
So the answer is 720x5 over 2 which gives 1800

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

sneha  (5 years ago)

5 peroids=5!=120
one extra subjects=5
total no of peroids=6
total=120*5*6=3600

Is this solution Helpfull? Yes (1) | No   

madhukar sharma  (10 years ago)

6p5*5c1=3600 is the right answer.. here is the link..http://books.google.co.in/books?id=a1-wnil6kTsC&pg=PA150&lpg=PA150&dq=If+there+are+Six+periods+in+each+working+day+of+a+school,+In+how+many+ways+can+one+arrange+5+subjects+such+that+each+subject+is+allowed+at+least+one+period?&source=bl&ots=ecMDGJ5Vbd&sig=_GCf7gMGQ61b6h1xXR3ATMCXSZM&hl=en&sa=X&ei=kKg-UrDLGY3NrQfLjYCoBg&ved=0CEkQ6AEwBw

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Chennakrishna Rayachoti  (9 years ago)

there are 5 subjects and 6 periods so 6P5=720 and for final period it can be any one of the 5 subjects so it has 5 possibilities so
ans=720*5=3600

Is this solution Helpfull? Yes | No (2)  

BASANT KUMAR  (9 years ago)

since each subject is allowed atleast once that means any of the five subject can be alloted each period and there is six period in one day
so,5*5*5*5*5*5=15625

Is this solution Helpfull? Yes | No (1)  

swati  (7 years ago)

5 subject can be selected from 5 subject in 5C5 ways
1 subject can be selected in 5C1 ways
and total 6 subject can be arrange in 6! ways
as 2 subject must be same
so req answer is (5C1*5C5*6!)/2!=1800

Is this solution Helpfull? Yes | No (1)  

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