If n biscuits are distributed among N different beggars, what is the probability that a particular baggar gets exactly r biscuits ?

\frac{^{n} C_{r} {(N - 1)}^{r}}{N^{n}}

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\frac{^{n} C_{r} {(N - 1)}^{n - r - 1}}{N^{n}}

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\frac{^{n} C_{r} {(N - 1)}^{n}}{N^{n}}

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\frac{^{n} C_{r} {(N - 1)}^{n - r}}{N^{n}}

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Solution

The correct option is C $\frac{^{n} C_{r} {(N - 1)}^{n - r}}{N^{n}}$
Total no.of ways = $N^{n} .$ [Note. That first biscuit can be given to any of the N baggars.
Similarly second biscuit can also be given to any of the N beggars and so on].
Favourable no.of ways is $^{n} C_{r} . {(N - 1)}^{n - r} .$
Out of n biscuits, r biscuits can be given to a particular beggar in $^{n} C_{r}$ ways and the remaining n-r biscuits can be distributed among the remaining n-r biscuits can be distributed among the remaining N-1beggars in ${(N - 1)}^{n - r}$ ways.
Hence the required probability $= \frac{^{n} C_{r} {(N - 1)}^{n - r}}{N^{n}} .$

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