Let j and n be positive integers with j = n. An experiment consists of choosing

Let j and n be positive integers with j = n. An experiment
consists of choosing at random a j-tuple of positive integers whose sum is at
most n.(a) Find the size of the sample space. Hint: Consider n
indistinguishable balls placed in a row. Place j markers between consecutive
pairs of balls with no two markers between the same pair of balls. (We also
allow one of the n markers to be placed at the end of the row of balls.) Show
that there is a 1-1 correspondence between the set of possible positions for the
markers and the set of j-tuples whose size we are trying to count.(b) Find the probability that the j-tuple selected contains
at least one 1.