Find the number of permutations

Question:

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

Solution:

Permutations of n distinct things taken r together =nCr

And when 3 particular things must occur together, we get,

n – 3Cr – 3

n – 3Cr – 3 × (r – 2)! × 3!

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