Seem like these are more statistical

a. How many permutations of the seven letters A,B,C,D,E,F,G are there? b. You have a pile of 20 identical blank cards. On each card you draw a circle, a plus, or a square. How many piles of 20 cards are possible? c. Find the next four largest 4-combinations of the set {1,2,3,4,5,6,7,8} after {1,2,3,5}. d. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace?

Prove the follwoing

Show that every positive integer can be written as the product of two numbers. One is the power of 2 and one is odd.

Integers

suppose that integers 1,2,3,4,5,6,7,8,9,10 are arranged randomly along a circle. 1) show that For each circular arrangement, there exists at least three adjacent numbers whose sum is greater than 17 2) take n + 1 integers from {1,2,3,....., 2n}. Show there exist two integers, one divides the other completely.

Divisibility

Suppose A divides N and B divides N. Does this always imply: A * B divides n? Now the question is under what condition A*B will always divide N? Prove it.

Fibonacci sequence

Please look at the attached file