1) How many positive integers less than \(100,000\) are odd and have a first digit greater than \(4\)?
2) Using a standard deck of playing cards, how many \(5\) card hands can be made so that:
a) there are \(3\) red cards and \(2\) black cards.
b) there are \(2\) aces.
c) there are \(2\) of one suit and \(3\) of a different suit.
d) there are at least \(2\) spades.
3) How many distinguishable permutations can be found in the word RIDDLER?
4) You and \(9\) of your classmates need to get together for a group project. How many different ways could all of you sit at a round table?
5) The bookstore in downtown Naperville is arranging books on the front table. There are \(3\) suspense books, \(2\) action books, and \(4\) romance novels.
a) How many ways can all of the books be arranged?
b) How many ways could the books be arranged if each type of group should stay grouped together?
6) How many positive integer factors does \(50,000\) have?
7) How many positive odd integers less than \(1,000\) can be made from \(0\), \(2\), \(5\), \(6\), \(7\)?
8) \(8\) friends have \(2\) tickets to a Chicago Blackhawks game. How many ways can the two friends be seated at the game?
9) Solve for \(x\) without a calculator: \(12!-4\cdot11!+10!=10!\cdot x\).
10) How many circular arrangements of size \(4\) taken from Linda, Steve, Katie, Nate, Ari, and Jude are there?
11) How many ways can \(12\) keys be arranged on a key ring?
12) Consider the set of numbers: \(\left\{2,\ 3,\ 5,\ 9,\ 13,\ 15\right\}\).
a) How many subsets contain no two digit numbers?
b) How many subsets contain at least one two digit number?
Solution Bank
2) Using a standard deck of playing cards, how many \(5\) card hands can be made so that:
a) there are \(3\) red cards and \(2\) black cards.
b) there are \(2\) aces.
c) there are \(2\) of one suit and \(3\) of a different suit.
d) there are at least \(2\) spades.
3) How many distinguishable permutations can be found in the word RIDDLER?
4) You and \(9\) of your classmates need to get together for a group project. How many different ways could all of you sit at a round table?
5) The bookstore in downtown Naperville is arranging books on the front table. There are \(3\) suspense books, \(2\) action books, and \(4\) romance novels.
a) How many ways can all of the books be arranged?
b) How many ways could the books be arranged if each type of group should stay grouped together?
6) How many positive integer factors does \(50,000\) have?
7) How many positive odd integers less than \(1,000\) can be made from \(0\), \(2\), \(5\), \(6\), \(7\)?
8) \(8\) friends have \(2\) tickets to a Chicago Blackhawks game. How many ways can the two friends be seated at the game?
9) Solve for \(x\) without a calculator: \(12!-4\cdot11!+10!=10!\cdot x\).
10) How many circular arrangements of size \(4\) taken from Linda, Steve, Katie, Nate, Ari, and Jude are there?
11) How many ways can \(12\) keys be arranged on a key ring?
12) Consider the set of numbers: \(\left\{2,\ 3,\ 5,\ 9,\ 13,\ 15\right\}\).
a) How many subsets contain no two digit numbers?
b) How many subsets contain at least one two digit number?
Solution Bank