There are n different gift coupons, each of which can occupy N(N > n) different…
Mathematics · JEE Advanced · NTA Exams — Statistics and Probability
There are n different gift coupons, each of which can occupy N(N > n) different envelopes, with the same probability 1/N
P1: The probability that there will be one gift coupon in each of n definite envelopes out of N given envelopes
P2: The probability that there will be one gift coupon in each of n arbitrary envelopes out of N given envelopes
Consider the following statements
(i) P1 = P2 (ii) P1 = \(\frac{\mathrm{n}!}{\mathrm{N}^{\mathrm{n}}}\) (iii) P2 = \(\frac{N!}{N^{n}(N-n)!}\)
(iv) P2 = \(\frac{n!}{N^{n}(N-n)!}\) (v) P1 = \(\frac{\mathrm{N}!}{\mathrm{N}^{\mathrm{n}}}\)
Now, which of the following is true
P1: The probability that there will be one gift coupon in each of n definite envelopes out of N given envelopes
P2: The probability that there will be one gift coupon in each of n arbitrary envelopes out of N given envelopes
Consider the following statements
(i) P1 = P2 (ii) P1 = \(\frac{\mathrm{n}!}{\mathrm{N}^{\mathrm{n}}}\) (iii) P2 = \(\frac{N!}{N^{n}(N-n)!}\)
(iv) P2 = \(\frac{n!}{N^{n}(N-n)!}\) (v) P1 = \(\frac{\mathrm{N}!}{\mathrm{N}^{\mathrm{n}}}\)
Now, which of the following is true
- Only (i)
- (ii) and (iii)
- (ii) and (iv)
- (iii) and (v)
Answer
(B) (ii) and (iii)
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