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Find the number of permutations of n dis...

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

Text Solution

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The correct Answer is:
`.^(n-3)C_(r-3)xx(r-2)!xx3!`
Total number of things=n
We have to arrange r things out of n in which three particular things must occur together.
Therefore, comnination of n things taken r at a time in which 3 things always occurs `= .^(n-3)C_(r-3)`
If three things taken together, then it is considered as 1 group.
Arrangement of these three things =3!
Now, we have to arrange =(r-3)+1=(r-2) objects
`therefore` Arrangement of (r-2) objects =(r-2)!
`therefore` Total number of arrangements `= .^(n-3)C_(r-3)xx(r-2)!xx3!`
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