Problem 1
How many license plates can be made using two uppercase letters followed by a 3 -digit number?
Problem 1
How many permutations are there for the letters of the name Bathsheba? Solomon? Ahab? your own name?
Problem 1
A "word" is a string of one or more lowercase letters. How many words can be formed using all the letters of the word hyperbola? In how many words will \(h\) and \(y\) occur together? In how many will \(h\) and \(y\) not occur together?
Problem 2
How many ways can you draw a club or a heart from an ordinary deck of cards? A spade or an ace? An ace or a jack? A card numbered 3 through 9 ? A numbered card (Aces are not numbered cards) or a king?
Problem 2
How many arrangements are possible for the letters of the following words: (a) Tennessee (b) Mississippi (c) Kansas (d) Oregon. (e) Manifoba (f) Vesitine
Problem 2
A bookshelf contains three novels, six books of poetry, and four reference books. In how many ways can these books be arranged so that the books of each type are together?
Problem 3
A shelf has room for 10 books. (a) Given an inventory of 25 books, how many years will it take to display all combinations of 10 books if the display is changed once a week? (b) How many years will it take if the display is changed five times a week?
Problem 3
How many ways can one choose one right glove and one left glove from six pairs of different gloves without obtaining a pair?
Problem 3
How many words or strings of 12 letters can be formed from the symbols $$a, a, a, a, b, b, b, b, b, b, b, b$$ provided that no two \(a\) 's can occur together?
Problem 4
Find the number of arrangements of the word engineering. (a) In how many of these are the three \(e\) 's together? (b) In how many of these are exactly two e's together?
