Combinatorics | Number Theory Answers

Find an explicit formula for the Fibonacci numbers.

How many bit sequences of length seven contain an even number of 0s?

Find a recurrence relation for the number of bit sequences of length n with an even number of 0s.

Show that the sequence 〖{a〗_n} is a solution of the recurrence relation a_n=a_(n-1)+〖2a〗_(n-2)+2n-9 if

(i)〖 a〗_n=-n+2

(ii) a_n=〖5(-1)〗^n-n+2

(iii) 〖3(-1)〗^n+2^n-n+2

(iv)〖7.2〗^n-n+2

Find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s. Find also the initial conditions?

Is the sequence 〖{a〗_n} a solution of the recurrence relation a_n=8a_(n-1)-16a_(n-2)if a_n=n^4 a_n=0.

In a company, ID cards have 5 digit numbers.


a) How many ID cards can be formed if repetion of the digit is allowed?


b) How many ID cards can be formed if repetion of the digit is not allowed?

A man has 3 different suits, 4 different shirts and 5 different pairs of shoes. In how many different ways can this man wear a suit, a shirt and a pair of shoes?

There are 3 different roads from city A to city B and 2 different roads from city B to city C. In how many ways can someone go from city A to city C passing by city B?

A student can select one of 6 different mathematics books, one of 3 different chemistry books and one of 4 different science books. In how many different ways can a student select a book of mathematics, a book of chemistry and a book of science?