# If there are 6 periods 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? while solving this problem why we write 6P5 ??????

Each of the arrangements which can be made by taking some or all of a number of things is called a Permutation.

There are 5 subjects, Hindi, English, Maths, Science and Social studies.

There are 6 periods.

The first period can be allotted to any of the 5 subjects.

That is, there are 5 different ways of allotting the first period.

Now one subject has been allotted.

The second period can be allotted to any of the 4 subjects.

That is, there are 4 different ways of allotting the second period.

Now two subjects have been allotted.

The third period can be allotted to any of the 3 subjects.

That is, there are 3 different ways of allotting the third period.

Now three subjects have been allotted.

The fourth period can be allotted to any of the 2 subjects.

That is, there are 2 different ways of allotting the fourth period.

Now four subjects have been allotted.

The fifth period can be allotted to 1 subject.

That is, there is onlye one way of allotting the fifth period.

Now five subjects have been allotted.

Thus, by the principle of counting there are different ways to allot 5 periods.

There are 6 periods in total.

Hence the 6th period can be allotted to any of the 5 subjects.

Thus, the total number of arrangements of 5 subjects in 6 periods is That is total number of arrangements is • -16

because there are 6 periods which in which only 5 subjects are allowed this is the way of permutation so we use that

• -8
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