$n$ biscuits of different shape and size are to be distributed to $N$ beggars at random. The probability that a particular beggar receives r(r < n) biscuits is

\frac{n_{C_{r}}}{N^{n}}

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\frac{n_{C_{r} \times^{n - 1} C_{n - r}}}{n_{C_{n}}}

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

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1 - \frac{n_{C_{r}}}{N^{n}}

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Solution

The correct option is D $\frac{n_{C_{r} \times (N - 1)^{n - r}}}{N^{n}}$
We can select $r$ biscuits from $n$ biscuits in $^{n} C_{r}$ ways.
The remaining $(n - r)$ biscuits can be distributed among the $(N - 1)$ beggars in ${(N - 1)}^{(n - r)}$ ways.
Therefore, required probability = $\frac{^{n} C_{r} * {(N - 1)}^{(n - r)}}{N^{n}}$

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Similar questions

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

Let r and n be positive integers such that $1 \leq r \leq n .$ Then prove the following :

(i) $\frac{^{n} C_{r}}{^{n} C_{r - 1}} = \frac{n - r + 1}{r}$
(ii) $n^{n - 1} C_{r - 1} = (n - r + 1)^{n} C_{r - 1}$
(iii) $\frac{^{n} C_{r}}{^{n - 1} C_{r - 1}} = \frac{n}{r}$
(iv) $^{n} C_{r} + 2^{n} C_{r - 1} +^{n} C_{r - 2} =^{n + 2} C_{r}$

Q. The value of

n \sum r = 1 \frac{r^{n} C_{r}}{^{n} C_{r - 1}}

Q. Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
(a)

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

(b) n ·_{^{n −}}_¹C_r_{− 1} = (n − r + 1) ⁿC_r_{− 1}
(c)

\frac{{}^{n}C_{r}}{{}^{n - 1}C_{r - 1}} = \frac{n}{r}

(iv) ⁿC_r + 2 · ⁿC_r_{− 1} + ⁿC_r_{− 2} = ^{n +}²C_r.

Q. Assertion :If

x =^{n} C_{n - 1} +^{n + 1} C_{n - 1} +^{n + 2} C_{n - 1} + . . . +^{2 n} C_{n - 1}

then

\frac{x + 1}{2 n + 1}

is integer Reason:

^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r} a n d^{n} C_{r}

is divisible by n if n and r are co-prime

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n biscuits of different shape and size are to be distributed to N beggars at random. The probability that a particular beggar receives r(r < n) biscuits is

The correct option is D nCr×(N−1)n−rNnWe can select r biscuits from n biscuits in nCr ways. The remaining (n−r) biscuits can be distributed among the (N−1) beggars in (N−1)(n−r) ways. Therefore, required probability = nCr∗(N−1)(n−r)Nn

$n$ biscuits of different shape and size are to be distributed to $N$ beggars at random. The probability that a particular beggar receives r(r < n) biscuits is