Question

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 with no further restrictions? b) How many solutions are there with all the x being odd and xi 3 7? iv) A certain course has a multiple choice exam consisting of 5 questions, each with 4 possible answers. Assume all the students attempt every question ow many students would have to be in the course for it to be certain that at least 3 students have chosen exactly the same sequence of answers to all 5 questions? Give reasons for your answer. v) For a particular 3-player card game, the 2 of clubs ( %2) is removed from a standard pack of cards. Then each of the 3 players are dealt a hand of 17 cards each a) How many 17 card hands contain exactly 8 clubs? b) How many 17 card hands contain exactly 8 hearts? c) Find the probability that a 17 card hand contains exactly 8 cards in at least one of the suits

Answer 1

(iu HATME NATI tS сь) eated.