(1 point) How many three-letter "words" can be made from 9 letters FGHIJKLMNII if repetition of letters (a) is allowed? Your answer is : (b) is not allowed? Your answer is : (1 point) In a cohort of 35 graduating students, there are three different prizes to be awarded. If no student can receive more than one prize, in how many different ways could the prizes be awarded? (1 point) A bit is a 0 or a 1. A bit string of length 8 is a sequence of 8 digits, all of which are either 0 and 1. (a) How many bit strings of length 8 are there? (b) How many bit strings of length 8 or less are there? (Count the empty string of length zero also.) (1 point) Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 7. (b) are divisible by 5 or by 7 (inclusive or). (c) are not divisible by either 5 or 7. (d) are divisible by 5 and by 7. (1 point) Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 7. (b) are divisible by 5 or by 7 (inclusive or). (c) are not divisible by either 5 or 7. (d) are divisible by 5 and by 7. (1 point) 3 mletter words" are formed using the letters A, B, C, D, E, F, G. How many such words are possible for each of the following conditions? (a) No condition is imposed. Your answer is : (b) No letter can be repeated in a word. Your answer is : (0) Each word must begin with the letter A. Your answer is : (d) The letter C must be at the end. Your answer is : (e) The second letter must be a vowel. Your answer is