The number of non-decreasing k-sequences on {1..n} is larger than the number of increasing k-sequences on {1..n} because entries may be repeated. If      a non-decreasing k-sequences on {1..n}, define...

The number of non-decreasing k-sequences on {1..n} is larger than the number of increasing k-sequences on {1..n} because entries may be repeated. If
   a non-decreasing k-sequences on {1..n}, define the sequence

By

(a) Show that the sequence Y is an increasing k-sequence on {1..(n þ k – 1)}.

(b) Show that if Y is any increasing k-sequence on {1..(n þ k – 1)} then there is an X as above that would be transformed into Y.

(c) Explain how this shows that the number of non-decreasing k-sequences on

/ If there are n different “kinds” of objects in a certain context, this allows

// us to count the number of selections of k objects where several objects

// of the same kind may be selected.