Question

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 allotted at least one period?

Answer 1

may be..6p5-6power5...im nt sure

Answer 2

Answer:

1800 ways

Step-by-step explanation:

There are 6 periods and 5 subjects. So 5 periods can be given the 5 subjects. That means 5 period for 6 subjects. That is 6P5.

Now the one period that is left could be filled using any of the 5 subjects. That is 1 subject from the 5 available. That would give as 5C1.

But this would cause repetition of a subject.

So our calculations would be :  

 $\\\frac{^6P_{5} . ^5C_{1}}{2!} = \frac{\frac{6!}{(6-5)!} . \frac{5!}{1! (5-1)!}}{2!}\\\\= \frac{\frac{6!}{1!} . \frac{5!}{1! . 4!} }{2!}\\\\= \frac{6! \frac{5.4!}{4!} }{2!}\\= \frac{6!.5}{2!} \\\\= \frac{6.5.4.3.2!.5}{2!}$

 = 6.5.4.3.5

 = 1800

Sorry for the small numbers :)