    Question

# The number of permutations of 20 dissimilar things taken not more than 10 at a time when repetitions are allowed is

A
2019(20201)
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B
2019(2010+1)
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C
2019(20101)
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D
2019(220+1)
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Solution

## The correct option is C 2019(2010−1)Let us find the number of permutations for selecting r objects (r≤10) from 20 dissimilar objects. Since, repetitions are allowed, each object can be selected in 20 ways. Hence, total number of permutations =20r. We can vary r from 1 to 10.Hence, total number of permutations =20+202+...+2010=2019(2010−1)This is a geometric series, with a=20, r=20, n=10Hence, Number of Permutations =arn−1r−1Number of Permutations =20(2010−119)Hence, option C is correct.  Suggest Corrections  0      Similar questions  Related Videos   Permutations
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