Combinatorics | Number Theory Answers

• Show that there are infinitely many primes p≅ 4(mod15).

A student purchases the following lock. There are 40 numbers. The three number key cannot use the same number twice. How many possible 3 digit keys are possible for this lock?

There are 11 soccer balls in the bag. You are going to pick out 5 balls for your students to use. How many different groups of 5 soccer balls can be chosen?

Eight friends go to a football game. How many different ways can they arrange themselves in their seats?

A man has 3 different suits, 4 different shirts and 5 different pairs of shoes. In how manyAct

different ways can this man wear a suit, a shirt and a pair of shoes?

In a certain country telephone numbers have 9 digits. The first two digits are the area

code (03) and are the same within a given area. The last 7 digits are the local number and

cannot begin with 0. How many different telephone numbers are possible within a given

area code in this country?

you choose one of the five-letter passwords producted by using the A,B,C,D and E,each letter should be used exactly once .what is the maximum number of password that do not have a letter in common with the password you chose (the same letter is not in the same place?)

Hint: if the question was asked for three-letter passwords created using the letters,A,B,and C the answer would be 2 :let the password you choose be ABC .passwords without a common letter:ABC 

a flage with five stripes will be prepaerd for a school team .we have red ,blue,yellow ,green ,black and brown.strips cannot be left colorless and no more than one used in a strip. the same color cannot be in the tow adjacent stripes.when the flag is inverted ,the colors should appear in the same order.example;blue|yellow|black|yellow|blue….how many different flags can be obtained under these conditions?

If a is prime, then a is irreducible, but not conversely test the validity of the statement.

How many hockey games would Leila have to schedule if there were 9 teams in a league and each team played each other three times.