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- The number of 5-element subsets from a set containing n elements is equal to the number of 6-element subsets from the same set. What is the value of n? (Hint: the order in which the elements for the subsets are chosen is not important.)In how many ways can we arrange all the letters in the word INFORMATION so that no pair of consecutive letters occurs more than once? (Note: IINNOOFRMTA is allowed but not INFORINMOTA, as IN occurs twice)The Martian language can be written in the familiar Roman alphabet, which has 21 consonants (B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z) and 5 vowels (A, E, I, O, U). All Martian nouns begin with a consonant, followed by one or more vowel-consonant pairs. However, no consonant can appear more than once in a single noun, and no vowel can appear more than once in a single noun. For example, VUX, DIYOK, and ZOBALUT are possible Martian nouns, but X, VUV, DIYIK, and ZEZELAL are not. How many Martian nouns are possible? Your answer must be a number. Briefly explain your answer. Recent expeditions to Mars have cast doubt on whether the Martian language can be written with exactly 21 consonants and 5 vowels. Suppose that Martian requires c consonants and v vowels, where c > 0, v > 0, and c > v. Express the number of possible Martian nouns in terms of c and v. Your answer need not be in closed form.
- How to use letters in pre algerbraHow many three-letter words (with or without meaning, without repetition of letters) are formed with the letters of the word TESTIM?On February 20, 2004, the Ohio Bureau of Motor Vehiclesunveiled the state’s new license plate format. The plateconsists of three letters (A–Z) followed by 4 digits (0–9).Assume that all letters and digits may be used, except thatthe third letter cannot be O, I, or Z. If repetitions are allowed,how many different plates are possible?
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- Standard license plates for passenger vehicles in California are of the form NMLMXXX where N is any digit except 0, X is any digit, L is any uppercase letter and M is any uppercase letter except I, O and Q. What is the minimal number of California licensed vehicles that need to be parked in a parking structure to guarantee that there are ten vehicles with the same first digit, last digit and the first letter in their license plate number? Assuming that all combinations of letters are allowed, what is the minimal number of vehicles in the structure that guarantees that at least ten have the license plate number beginning with 1, ending with 6 and having the first letter P?How many permutations of the letters " PAPUNTAPALANGTAYOSAEXCITINGPART" can be made?Pls select correct option and explain in 10-15 sentences only