3sir isnt the qn ask exactly three nos.
an unbiased die,with faces numbered 1,2,3,4,5,6 is thrown n times and 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 the list
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7 Answers
62no you have to chose 3 out of 6 numbers! so 1/2
and for exactly 3.. you have to add a couple of terms to get the value for exactly 3
19nishant, i am getting something which is very different from the answers posted here...
my working:
we can get (6n) lists of elementary events, each of length (n). out of all these elementary events, we need to select that list which has only three numbers out of {1,2,3,4,5,6} ...these 3 numbers can be selected in 6C3 ways !
...now by using three selected numbers, we can get 3n lists of elementary events , each of length (n). but these 3n lists may contain those lists which contain exacltly two numbers and exactly one number
the no. of lists of length (n) which contain exactly 2 nos. out of 3 chosen nos. = 3C2(2n -2)
the no. of lists of length (n) which contain exactly 1 no. out of 3 chosen nos. =3C1(1n) =3
thus the total number of lists of length (n) which contain three distinct nos. out of the six given numbers is 6C3{3n- 3C2(2n -2) -3 }
= 6C3{3n - 3.2n +3}
hence required probability is [6C3{3n - 3.2n +3}] / 6n
1organic sir ur right but i dint get the 2^n-2 part pls explain this is a 2002 iit problem
62number of ways in which you can construct a list of length n whcih contains 2 elements... = 2n
among them, 2 are those which include exactly one of the elements... (ie all the list contains either the 1st or the 2nd element)
eliminating these two cases, you get 2n-2