Let n be an odd integer. The \emph{median} of a sequence x1,…,xn, denoted of numbers, median(x1,…,xn), is the unique value x such that there are at least ⌈n/2⌉ values less than or equal to x and at least ⌈n/2⌉ values greater than or equal to x.

For example,

median(8,4,3,4,7,5,6)=5 since 4,3,4,5≤5 and 8,7,5,6≥5; and

median(8,5,3,4,7,5,6)=5 since 5,3,4,5≤5 and 8,5,7,5,6≥5.

Consider a uniform random sequence x1,…,x7 of 7 numbers each chosen from the set {1,2,3,…,10}

a. What is the probability that max{x1,…,x7} occurs exactly once in x1,…,x7?

I did:

n=7, that is 7*(1⁶+2⁶+3⁶+4⁶+5⁶+6⁶+7⁶+8⁶+9⁶) / 10⁷ = .6848835

b. What is the probability that median(x1,…,x7) occurs exactly once in x1,…,x7?

I'm a little confused with this one. My friends are getting around 0.47 but I don't understand how. I would appreciate any help.