The number of permutations of n distinct objects taken r at a time in which three particular objects occurs together

Question:

The number of permutations of n distinct objects taken r at a time in which three particular objects occurs together is ___________.

Solution:

Total number of objects (distinct) = n

Since, 3 objects are taken together (i.e 3 objects are together)

The number of ways of selecting distinct objects from n is nCr

If three objects occur together, then number of ways = n−3Cr−3

also number of arrangements of these three things = 3!

and number of arrangements of (− 3 + 1) objects = (r − 2)! 

∴ Total possible ways of taking r at a time from n objects such that three particular are together is n−3Cr−3 (r − 2)! 3!

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