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Question
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
Options
n − 3Pr − 3
n − 3Pr
nPr − 3
r ! n − 3Cr − 3
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Solution
r ! n − 3Cr − 3
Here, we have to permute n things of which 3 things are to be included.
So, only the remaining (n - 3) things are left for permutation, taking (r - 3) things at a time. This is because 3 things have already been included.
∴ Total number of permutations = r ! n − 3Cr − 3
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