PLEASE DO BOTH (9) (5 pts) How many solutions are there to the inequality 11 +*2+I3...
PLEASE DO BOTH (7) (5 pts) A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. How many ways are there to choose (a) a dozen croissants? (b) two dozen croissants with at least two of each kind? (8) (5 pts) How many solutions are there to the equation 11 +12+13 +In+ 15 + 16 = 29, where I, for i = 1,2,3,4,5,6, is a non-negative integer such that (a) Ii > 1...
PLEASE DO BOTH (5) (5 pts) Prove the identity (1) () = (x) (---), whenever n, r, and k are non-negative integers with rn andk Sr. (6) (5 pts) How many ways are there to select five unordered elements from a set with three elements when repetition is allowed?
please do both 4 and 5 and show work! will upvote fast Problem VII.4. How many non-negative integer vectors are there such that where exactly k of the entries zero? N Problem VII.5. Prove the following: () ik
5. Consider the equation: 10 sin(Tx)+5= 8 [2 pts.] a. How many solutions should we expect this equation to have on the interval 0 5x56? [6 pts.] Find all solutions to the equation on the interval 0 5x56.
I have 4 questions dont know can anyone help me with any of it? ii) Consider the 11 letter word MATHEMATICS a) How many distinct words can be formed by rearranging its letters? b) How many 4 letter words can be formed using the letters in the word MATHEMATICS, using letters no more often than they appear in the word? ii) Consider the equation where xi, x2, 13, T4,5 and re are non-negative integers a) How many solutions are there...
Question 5# (Combinations, including stars and bars') Problem: How many PINs have digit suam 20? (A PIN is string abcd of 4 decimal digits eg 6806) As a first attempt at answering this: (a) How many different solutions in non-negative integers has the equation a+b+c+d-20? Hint: 20 stars and 3 bars. The count in (a) is much too big for our problem because it includes many solutions that contain non-decimal digits; ie. values of a, b, c or d that...
PLEASE DO BOTH (1) (5 pts) How many ways can you permute the letters in BANANA? (2) (5 pts) At a Chinese restaurant, dinner for 8 people consists of 3 items from column A, 4 items from column B and 3 items from column C. If columns A, B and C have 5, 7 and 6 items respectively how many different dinner combinations are possible?
9. (5 points) Please describe an algorithm that takes as input a list of n integers and finds the number of negative integers in the list. 10. (5 points) Please devise an algorithm that finds all modes. (Recall that a list of integers is nondecreasing if each term of the list is at least as large as the preceding term.) 11. (5 points) Please find the least integer n such that f() is 0(3") for each of these functions f()...
Please answer question 3 Find all (infinitely many) solutions of the system of congruence's: Use Fermata little theorem to find 8^223 mod 11. (You are not allowed to use modular exponentiation.) Show that if p f a, then a^y-2 is an inverse of a modulo p. Use this observation to compute an inverse 2 modulo 7. What is the decryption function for an affine cipher if the encryption function is 13x + 17 (mod 26)? Encode and then decode the...