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

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

Solution:

${ }^{n} C_{r}$ = Permutations of $n$ distinct things taken $r$ together

And when three particular things must occur together, we obtain,

$\begin{array}{l} ={ }^{n-3} C_{r-3} \\ ={ }^{n-3} C_{r-3} \times(r-2) ! \times 3 ! \end{array}$

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