There are six periods in each working day of a school. Number of ways

Question

There are six periods in each working day of a school. Number of ways in which 5 subjects can be arranged if each subject is allotted at least one period and no period remains vacant is

(A) 210 
(B) 360 
(C) 1800
(D) 2100
(E) 3600

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

Gknight5603 · Answer

5c1*6c2*4*3*2*1= 1800 (C)

Posted from my mobile device

Gmatpractitioner · Answer

Answer is E - 3600 IMO

There are 6! ways to arrange the day (imagine the subjects are A,B,C,D,E and ?)
There are 5 option possible for '?'
So total arrnagement = 6! x 5 = 3600

CrackverbalGMAT · Answer

The 5 subjects can be allotted to 6 periods in 6C5 = 6C1 = 6 ways. These 5 subjects can then be arranged in 5! = 120 ways.

The 6th period can be allotted any 1 subject in 5 ways.

Therefore the total number of ways = 6 * 120 * 5 = 3600 ways

Option E

Arun Kumar

ScottTargetTestPrep · Answer

Solution:

If we let the five subjects be A, B, C, D, and E and let’s say A is repeated. So we can have, for example, ABCDEA for the six periods of the day. Of course, these six subjects (including the repeating subject A) can be arranged in 6! / 2! = 720/2 = 360 ways. However, since the repeating subject can be also B, C, D, or E, there are a total of 360 x 5 = 1800 ways to allot the 5 subjects for 6 periods without a vacant period.

Answer: C

griffith7 · Answer

Why are there 5 options for the "?" slot? What in the question stem tells us one of the subjects must be repeated to fill this slot? Couldn't there simply be a 6th unknown subject?

Regor60 · Answer

That would be assuming information not presented in the question stem.

The question refers only to 5 subjects.

It is not an assumption to believe no other subjects exist.

Posted from my mobile device

Dereno · Answer

There are 5 subjects and 6 periods. Each subject should be given one period at least.

So, only one slot remains vacant. That 1 slot can be filled by any of the 5 subjects.

Choose that one subject which is going to recur =  5C1 = 5

After choosing you will get the subjects as : ABCDE(A).

I have assumed the subjects to be A B C D E and the subject which is recurring as A .

Now arrange it = 6 periods can be arranged in  6! Ways

And a subject is recurring = 6!/2

Total ways = 5* (6!/2) = 5*6*5*4*3 = 25*4*6*3 = 100*18 = 1800

Option C

Sijojohnn · Answer

hey there are 6 places and we need to fill everything at least one from the five so we can only do one subject 2 times. thus 6!divided by 2! to eliminate the common to get for one subject occurring twice gives 360 then multiply by 5 to get total 1800

Gknight5603

5c1*6c2*4*3*2*1= 1800 (C)

Posted from my mobile device

There are six periods in each working day of a school. Number of ways

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

There are six periods in each working day of a school. Number of ways

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards