A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point

there will be 2 cases,
6 steps forward;5 steps backward

6 steps backward;5 steps forward
= reqd. probability
= 11C6 * (0.4)^6 * (0.5)^5 + 11C6 * (0.4)^5 * (0.6)^5

= 11C5 * (0.4)^5 * (0.6)^5 * (0.4 + 0.6) ... [11C6 = 11C5]

= (11x10x9x8x7)/(1x2x3x4x5) * (0.24)^5

= 0.368.