Show that there is a one-to-one correspondence between the

Question

Question: (a) Show that there is a one-to-one correspondence between the number of ways to put ten identical marbles into three boxes and the number of ordered triples (x, y, z) of nonnegative integers which satisfy x+ y+ z= 10.

(b) How many triples (x, y, z) of nonnegative integers satisfy x + y + z = 10?

(c) How many 5-tuples (x, y, z, u, v) of nonnegative integers satisfy x + y + z + u + v = 19?