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Grade 11Algebra

An unbiased die, with faces numbered 1, 2, 3, 4, 5, 6, is thrown n times and the list of n numbers showing up is noted. What is the probability that, among the numbers 1, 2, 3, 4, 5, 6, only three numbers appear in this list?

Profile image of Simran Bhatia
12 Years agoGrade 11
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1 Answer

Profile image of Aditi Chauhan
12 Years ago
Hello Student,
Please find the answer to your question
The total no. of outcomes = 6n
We can choose three numbers out of 6 in 6 C3 ways. By using three numbers out of 6 we can get 3n sequences of length n. But these sequences of length n which use exactly two numbers and exactly one number.
The number of n – sequences which use exactly two numbers
= 3 C2 [2n – 1n – 1n] = 3(2n – 2) and the number of n sequence which are exactly one number
= (3 C1) (In) = 3
Thus, the number of sequences, which use exactly three numbers
= 6 C3 [3n – 3(2n – 2) – 3] = 6 C3 [3n – 3(2n) + 3]
∴ Probability of the required event,
= 6 C3 [3n – 3(2n) + 3]/6n

Thanks
Aditi Chauhan
askIITians Faculty

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