4. Let x, y and z be integers between 0 and 9. How many ways can x, y, z be chosen such that xyz is odd?
5. What conditions on n, k need to hold so that n(n −1) ···(n −k + 1) =n!
(n−k)!is a true statement? Write this as a theorem and prove it.
6. Calculate ∫∞0xne−xdx for n = 0, 1, 2, 3, 4 (start with n = 0, and then
do integration by parts for n = 1 etc.) Give a formula for this integral
for n an arbitrary nonnegative integer. (You do NOT need to prove
this, just give a formula.)