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Comprehension- \( \quad \) Consider the experiment of distribution of balls among urns. Suppose ...
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Comprehension- \( \quad \) Consider the experiment of distribution of balls among urns. Suppose we are given \( M \) urns, numbered 1 to \( M \), among which we are to distribute \( \mathrm{n} \) balls \( (nM) \). Let \( P(A) \) denote the probability that each of the urns numbered 1 to \( \mathrm{n} \) will contain exactly one ball. Then answer the following questions.
If the balls are identical and any number of balls can go to any urns then \( P(A) \) equals
(a) \( \frac{1}{M^{n}} \)
(b) \( \frac{1}{{ }^{M+n-1} C_{M-1}} \)
(c) \( \frac{1}{M+n-1} C_{n-1} \)
(d) \( \frac{1}{{ }^{M+n-1} P_{M-1}} \)
If the balls are identical and any number of balls can go to any urns then \( P(A) \) equals
(a) \( \frac{1}{M^{n}} \)
(b) \( \frac{1}{{ }^{M+n-1} C_{M-1}} \)
(c) \( \frac{1}{M+n-1} C_{n-1} \)
(d) \( \frac{1}{{ }^{M+n-1} P_{M-1}} \)
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