Practice:

Review the concepts of permutations, r-permutations and combinations.

a)  How many permutations of {a,b,c,d,e,f,g} end with a?



b) How many different ways are there to choose a president, vice president and treasurer out of 10 people?



c) How many ways are there to choose a committee of 5 people out of nine people?



Exercises:


1: How many positive integers between 5 and 31:

1.1) are divisible by 3?



1.2) are divisible by 4?



1.3) are divisible by 3 or 4?




2: How many bit strings of length 12 contain:

2.1) exactly four 1s?




2.2) at most four 1s?




2.3) at least four 1s?




2.4) an equal number of 0s and 1s?




3) If there is a room with 36 people and every person shakes hands with every other person exactly once, how many handshakes are there in all?




4) How many ways can a set of three positive integers less than 100 be chosen?





5) A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17 are true. If the questions can be positioned in any order, how many different answer keys are possible?





6) If a password is made up of lowercase letters or digits, how many passwords of length 6 are there that contain AT LEAST two digits?




7)  How many permutations of the letters ABCDEFG contain
    - the string BCD?
    - the strings BA and GF?




8)  The English alphabet continas 21 consonants and 5 vowels.  How many
	strings of 6 lowercase letters of the English alphabet contain:

	a) exactly one vowel?



	b) exactly 2 vowels?



	c) at least one vowel?



	d) at least 2 vowels?