A box contains 10 light bulbs. Find the number of n of ordered samples of (a) size 5 with replacement, and (b) size 5 without replacement.

How many positive integers can be formed from the digits 1, 2, 3, and 4 if no digit is repeated in any one integer?

Find the number of n ways that a company consisting of 30 members can elect a president, vice-president, and secretary (assuming that no one person can be elected to more than one position).

There are four train lines between X and Y; and three train lines between Y and Z. Find the number of ways a person can travel:

(1) by train from X to Z by way of Y

(2) roundtrip by train from X to Z by way of Y

How many ways can the roundtrip by train be taken from X to Z by way of Y, given that you do not use the same train line more than once?