Quiz 4:  Practice Test Chapter 10:   Counting Principles         MGF 1106         Ambrioso


You should work on the homework as well as the Practice Test at the end of Chapter 10.


1.               Evaluate P(5, 3).


2.               Evaluate C(7, 3).


3.               Evaluate



4.               In how many ways can two letters be chosen from the alphabet?


5.               Suppose two dice are thrown.  In how many ways can you get a sum of ten?


6.               Four people are to pose for a group picture.  How many different arrangements are possible if they are to stand in a single row?


7.               How many counting numbers less than 450 are divisible by 2 or 3?


8.               How many subsets of 4 elements does the set { a, b, c, d, e, f } have?


9.               How many distinct arrangements of the letters in the word “letter” are possible?


10.            How many different sums of money can be made from a penny, a nickel, a dime, a quarter, and a half-dollar, and a dollar bill if exactly four of these are selected?


11.            Given a set with 8 elements.  How many subsets of less than 3 elements does it have?


12.            You are putting a square slide into a slide projector.  How many way can you orient the slide?  Note that we are counting all orientations.  Only one of them is correct.


13.            Draw a tree diagram illustrating the possible outcomes if two letters are chosen from the set {a, b, c } with no repetitions allowed?


14.            You wish to make a small lottery (played like the Florida lottery) for a group of young students.   It will have 20 numbers and each child will chose 4.  How many possibilities are there?


15.            A motorcycle license plate consists of 3 letter followed by 2 numbers.   How many plates are possible?


16.            Suppose you have six textbooks and wish to arrange two of them on a shelf.  In how many ways can you arrange them?


17.            There are seven women on committee.  How many subcommittees an be formed if we must have 3 women on the subcommittee?


18.            If 2 married couples are to be arranged in a row, with the couples sitting together, how many arrangements are possible?


19.            In how many ways can two spades be drawn if order is taken into consideration?


20.            A committee of six students is to be formed by choosing from a group of 5 boys and 7 girls.  If the committee must have 3 boys and 3 girls,  how many different committees are possible?