Problem 4 How many different signals, each consisting of 8 flags hung in a vertical line can be formed from a set of 4 red flags, 3 white flags and a blue flag? a . If all flags of the same color are distinguishable? b . If all flags of the same color are identical? Problem 5 How many 3-letter words with or without meaning, can be formed out of the letters of the word, LOGARITHMS', a. If repetition of letters is allowed? b. If repetition of letters is not allowed? Problem 6 a. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? b. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? Problem 7 Five high-profile guests, A, B, C, D and E, are invited to a corporate dinner party. a. In how many ways can these 5 people be seated at a round table? b. In how many ways so that A and B must always sit together. C. In how many ways so that C and D must not sit together