Question

from a group of n objects r objects are taken at a time in which K particular objects are always included In how many ways it could be done ​

Answer 1

Answer:

This can be done in three ways.

This is called restricted permutation.

The ways are given in the image.

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Answer 2

Concept:

A Permutation is an organisation of its members into a sequence or linear order, or a rearrangement of its elements if the set is already sorted.

Given:

There are n objects and r objects need to be selected which includes k particular objects.

Find:

The number of possible ways to select the objects.

Solution:

The total number of objects = n.

The total number of objects that need to be selected = r.

The number of objects that need to be always included = k.

Taking k objects into one group, then the total number of objects remaining is = n - k.

The number of objects to select = r - k.

There are r places to fill the selected objects.

The number of ways to select is = $^{n-k}P_{r-k} *r$.

Hence, the number of ways is $^{n-k}P_{r-k} *r$.