the number of ways in which the time table for monday we completed there must be 5 lessons that day that is algebra geometry characters trigonometry vectors and Algebra and geometry must not immediately follow each other
the number of ways in which the time table for monday we completed there must be 5 lessons that day that is algebra geometry characters trigonometry vectors and Algebra and geometry must not immediately follow each other
Can't understand the query but this might be the solution .
If there are 6 periods in each working day of a school. In how many different ways can one arrange 5 subjects such that each subject is allowed at least one period?
Soln:-
Lets think how we might pick this time table we can first assign a slot for each of our five subjects then finally pick the subject for the remaining slot.
Subject A has a choice of 6 slots
Subject B has a choice of 5 slots
Subject C has a choice of 4 slots
Subject D has a choice of 3 slots
Subject E has a choice of 2 slots
So far we have created 6!=7206!=720 distinct permutations and there is a choice of 5 subjects for the remaining slot creating 5⋅720=36005⋅720=3600 possible permutations but we note that these are not all distinct because we could swap the repeated subject with itself in the other slot the total number of distinct timetables is therefore 36002=1800.
Can't understand the query but this might be the solution .
If there are 6 periods in each working day of a school. In how many different ways can one arrange 5 subjects such that each subject is allowed at least one period?
Soln:-
Lets think how we might pick this time table we can first assign a slot for each of our five subjects then finally pick the subject for the remaining slot.
Subject A has a choice of 6 slots
Subject B has a choice of 5 slots
Subject C has a choice of 4 slots
Subject D has a choice of 3 slots
Subject E has a choice of 2 slots
So far we have created 6!=7206!=720 distinct permutations and there is a choice of 5 subjects for the remaining slot creating 5⋅720=36005⋅720=3600 possible permutations but we note that these are not all distinct because we could swap the repeated subject with itself in the other slot the total number of distinct timetables is therefore 36002=1800.
