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A man takes a step forward with probability 0.4 & backward with probability 0.6. Probability that at end of eleven stops he is one step away from

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A man takes a step forward with probability 0.4 & backward with probability 0.6. Probability that at end of eleven stops he is one step away from starting point is (i)`.^11C_6(0.24)^6` (ii) `.^11C_6(0.4)^6(0.6)^5` (iii) `.^11C_5(0.4)^5(0.6)^5` (iv) N.O.T Select the correct answer from above options

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Correct Answer - A::B::C::D The man will be one step away from the starting point, if (i) either he is one step ahead or (ii) one step behind the starting point. The man will be one step ahead at the ebnd of eleven steps, if he moves six steps forward and five steps backward. The probability of this event is `overset(11)""C_(6)(0.4)^(6)(0.6)^(5)+overset(11)C_(6)(0.6)^(6)(0.4)^(5)=overset(11)""C_(6)(0.24)^(5)`

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