Question

if there are 6 period 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?​

Answer 1

Answer:

1800 ways

Step-by-step explanation

We know we have 5 subjects and need to fit them on six periods, so there has to be one and only one repeated subject in order to fill both criteria:

1. All periods must be occupied

2. All subjects of of the 5 must be there at least once.

So, fist we understand that there is a pair of one subject within those 6 periods and can be arranged in different ways, ⁶C₂=15 ways

Next, we know that 5 subjects must be arranged so all 5 must be included,

5!= 5*4*3*2*1=720

finally

we multiply both possibilities

720*15= 1800 ways.