Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :

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Answer: B. {{5} \over {33}} Out of 11 consecutive natural numbers either 6 even and 5 odd numbers or 5 even and 6 odd numbers. Let, E = Even O = Odd Case-1 : E, O, E, O, E, O, E, O, E, O, E 2b = a + c \Rightarrow Even \Rightarrow Both a and c should be either even or odd. P = {{{}^6{C_2} + {}^5{C_2}} \over {{}^{11}{C_3}}} = {5 \over {33}} Case -2 : O, E, O, E, O, E, O, E, O, E, O P = {{{}^5{C_2} + {}^6{C_2}} \over {{}^{11}{C_3}}} = {5 \over {33}} Total probability = {1 \over 2} 	imes {5 \over {33}} + {1 \over 2} 	imes {5 \over {33}} = {5 \over {33}}

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :

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