3. (20 pts)How many ways are there to pass out 20 pencils (assume all the pencils are identical the same) to six children?

3.    (20 pts) How many ways are there to pass out 20 pencils (assume all the pencils are identical the same) to six children? Base on the following condition:

a)    No restriction. ( i.e. each kid may receive zero to 20 pencils.)

b)   Every child receives at least one pencil.

c)    None of child receives the same number of pencils.

d)   If the pencils are given out randomly. What is the probability that there are at least two kids receive the same number of pencils if every kids receives at least one pencil?

discrete math