There are 5 subjects to be taught on 1 working day in a school where the working day comprises 6 periods.Tell the no: of ways in which this can be done such that each subject gets atleast one period .

720

I am going for 600

its wrong!

720 hola

720, 600 Both are wrong!

1800?

Oh, no! That's not right..I overlooked the problem.

Maybe it's 30 for a single day.

21

So far all the answer are incorrect. But slackdemic, you are right for one reason. But thats not the exact answer.

144 different ways. (O:

could be 300?

One way u were thinking was:
we assign 5 periods to the 5 subjects in 6P5 ways : 720 ways
the remaining period can get ne one subject in 5 ways .
so total no. of ways = 720 * 5 = 3600 ways


Second way was:
Each of 5 subjects has to be given atleast 1 period , so no: of ways 5 subjects fit to 5 peiods is 5P5 =120 .
Then the remanining period can be filled in 5 ways ( considering that the ramining period has to have 1 subject and is not free) .
That makes it 120 *5 =600 .
This whole thing can be done in 6 ways , i.e either of the six periods could be the one which we are calling the remaining period.
Hence 6*600 =3600 .
Had it been possible that the remaining period is vacant , then the answer would have been 120*6*6 =4320


Slackdemic:
the 6 periods where 2 r idenctical can be taught in 6!/2! = 360 ways
there r 5 subjects and any of them can have 2 periods, so the ans is 360*5 = 1800
coz your method is not taking into account dat :
suppose subject maths has 2 periods in a day at 1st and 2nd periods........
then ur method counts this twice[ie 1st & 2nd period and 2nd & 1st period as separate]........coz u r treating maths at 1st and 2nd perids as different subjects.........which is wrong
......so ur answer shud be divided by 2........ This might be ur solution.