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A school period is a block of time allocated for lessons

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A school period is a block of time allocated for lessons  [#permalink]

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New post Updated on: 08 Aug 2018, 06:49
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A
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C
D
E

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Question Stats:

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A school period is a block of time allocated for lessons, classes in schools. There are 6 periods in each working day of school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period ?

A) 3600
B) 1800
C) 1400
D) 4000
E) 2000

Originally posted by LMP on 08 Aug 2018, 06:08.
Last edited by generis on 08 Aug 2018, 06:49, edited 1 time in total.
Edited the question, renamed topic
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Re: A school period is a block of time allocated for lessons  [#permalink]

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New post 08 Aug 2018, 06:32
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Bulusuchaitanya wrote:
A school period is a block of time allocated for lessons, classes in schools. There are 6 periods in each working day of School . In how many ways can one organize 5 subjects such that each subject is allowed at least one period ?

+1 for B.

5 subjects in 6 periods = 6P5
Remaining 1 period = 5P1

Since one subject is repeated twice, we need to divide the final arrangement by 2!

Total number of arrangement = ( 6P5 * 5P1 ) / 2! = 1800

Hence, B.
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Re: A school period is a block of time allocated for lessons  [#permalink]

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New post 08 Aug 2018, 08:07
Bulusuchaitanya wrote:
A school period is a block of time allocated for lessons, classes in schools. There are 6 periods in each working day of school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period ?

A) 3600
B) 1800
C) 1400
D) 4000
E) 2000


OA:B

Time slot................X X X X X X
Subject choice.........5 4 3 2 1 -

Empty slot can be arranged in 6 position :X X X X X X;X X X X X X;X X X X X X;X X X X X X;X X X X X X; X X X X X X
Empty Slot can be filled any of 5 subject,this will lead to 2 slots having same subjects

Total number of schedule of subject possible: \(\frac{5*4*3*2*1*(6*5)}{2!}=\frac{3600}{2}=1800\)
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Re: A school period is a block of time allocated for lessons  [#permalink]

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New post 09 Aug 2018, 03:12
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I have different way to solve the problem:
Number of period = 6
Number of subject = 5
So let's say 5 subject are A,B,C,D,E. We know atleast 1 subject has to be repeated.
If subject A is repeated. The AABCDE. by anagraming 6!÷2!.
No. Of ways = same can be true for all 5 subjects.
5×6!÷2!= 1800

Posted from my mobile device
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Re: A school period is a block of time allocated for lessons  [#permalink]

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New post 09 Aug 2018, 04:31
Bulusuchaitanya wrote:
A school period is a block of time allocated for lessons, classes in schools. There are 6 periods in each working day of school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period ?

A) 3600
B) 1800
C) 1400
D) 4000
E) 2000



Let the subjects be A, B, C, D, E & we have 6 periods to fill in. Hence one empty slot of period that can be filled by each of the 5 different periods.

Hence the arrangements will be of the form A B C D E _ , the empty slot "_", to be filled in by each subject as ( A B C D E A, A B C D E B, etc.)

Each of the arrangement can be re arranged within itself in 6!/2! ways

We get # of ways of organizing the periods as = (6!/2!) * 5 = 1800


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Re: A school period is a block of time allocated for lessons &nbs [#permalink] 09 Aug 2018, 04:31
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