$n$ biscuits are distributed among $N$ boys at random. The probability that particular boy gets $r (< n)$ biscuits is

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

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

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^{n} C_{r}

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\frac{r}{n}

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Solution

The correct option is A $^{n} C_{r} {(\frac{1}{N})}^{r} {(\frac{N - 1}{N})}^{n - r}$
It is a case of Bernoulli trails with number of trails $n$ and probability $= \frac{1}{N} ($ a success in one trail $)$
$∴ P (r$ success $) =^{n} C_{r} \times q^{n - 1} \times p^{r} =^{n} C_{r} \times {(1 - p)}^{n - r} \times p^{r}$
$=^{n} C_{r} \times {(1 - \frac{1}{N})}^{n - r} \times {(\frac{1}{N})}^{r} =^{n} C_{r} {(\frac{1}{N})}^{r} {(\frac{N - 1}{N})}^{n - r}$

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Similar questions

n

N

1 \leq r \leq n

{^{n} C}_{r} + {^{n} C}_{r - 1} = {^{n + 1} C}_{r}

\sum_{r = 0}^{n - 1} \frac{^{n} C_{r}}{^{n} C_{r} +^{n} C_{r + 1}}

^{n} C_{r - 1} = 36,^{n} C_{r} = 84

^{n} C_{r + 1} = 126

^{r} C_{2} = 8

^{n} C_{r} =^{n} C_{n - r}

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