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# 100. How many are even? How many are divisible by 5? How many are divisible by 3? How many are divisible by either 2 or 5 (possibly both)? How many

100. How many are even? How many are divisible by 5? How many are divisible by 3? How many are divisible by either 2 or 5 (possibly both)? How many are divisible by 2, 3, or 5? (9) In how many zeroes does the number 100! End? (10) How many different ways can the letters a, b, c, and d be lined up if each letter is to be used exactly once? What if we add the restriction that the letter b does not come immediately before the letter c? What if the letter b must come after the letter c but not necessarily immediately after? (11) Five cards are selected from a deck of 52 cards to form a poker hand. How many poker hands are possible? (12) Suppose D is a set containing n elements and S is a set containing k elements. How many different functions f are there with domain D such that f (x) S for every x D (in other words, how many different functions are there mapping D into S)? How many of these are one-to-one functions (so that f (x) = f (y) whenever x = y)? How many are one-to-on