Home
Class 11
MATHS
In the permutations of n things r, taken...

In the permutations of n things r, taken together, the number of permutations in which m particular things occur together is `""^(n-m)P_(r-m)xx""^(r)P_(m)`.

Text Solution

Verified by Experts

False
Arrangement of n things, taken r at a time in which m things occur together, we considered these m things as 1 group.
Number of object excluding those m objects = (r - m)
Now, first we have to arrange (r-m+1) objects.
Number of arrangements `=(r-m+1)"!"` and m objects which we consider as 1 group, can be arranged in `m"!"` ways.
`therefore` Required number of arrangements `=(r-m+1)"!" xx m"!"`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    NCERT EXEMPLAR|Exercise Matching The Columns|5 Videos

  • PERMUTATIONS AND COMBINATIONS

    NCERT EXEMPLAR|Exercise Fillers|9 Videos

  • MATHEMATICAL REASONING

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|21 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|5 Videos

Similar Questions

Explore conceptually related problems

STATEMENT-1 :The total number of combinations of n thing by taking some or all is 2^(n) . STATEMENT -2 : 5 identical balls can be distributed among 10 identical boxes in only one way if not more than one ball can go into a box. STATEMENT-3 : In the permutations of n things taken r at a time , the number of permutations in which m particular things occur together is ""^(n - m)P_(r - m) * ""^(r)P_(m)

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

f four xx the number of permutations of n things 3 togetherisecuar to five xx the number of permutations ofn -1 things 3 together,find

Find the number of permutations of n things taken r at a time in which two particular things : (i) always occur (ii) never occur.

Find the number of permutations of n things, taken r at a time, in which 3 particular things : (i) always occur (ii) will never occur.

If four xx the number of permutations of n things 3 together is equal to five xx the number of permutations of n-1things 3 together,find n.

Prove that the number of combinations of n things taken r at a time in which p particular things always occur is .^(n-p)C_(r-p)

Find the number of permutations of n different things taken r at a time such that two specific things occur together?