Find the number of five-letter words that use letters from {A, B, C, ..., Z} in which the letter A occurs at least once.
Find the number of five-letter words that use letters from {A, B, C, ..., Z} in...
can you please explain the solution clearly? thanks. LETTER COUNT The letter count of a number is defined as the number of letters in English spelling of that number. Letters in linking words such as 'and' are not counted. Find the largest number having these properties: -Its letter count is same as sum of the letter counts of each of its digits. No digit is used more than twice. -Does not start with zero. Exampe: 5010 FIVE THOUSAND TEN" has...
9. How many 10-letter words are there in which each of the letters e, n, r , s occur (a) At most once? (b) At least once?
Q3. Suppose a language containing five letters: A, B, C, D, E (5%) (b) How many four-letter words can you form if each letter appears only once in each word? (5%) (c) What is the probability that a three-letter word (with each letter appearing only once) con (a) How many three-letter words can you form in this language? tains E? (5%)
3. Consider rearranging the letters in the word "FATHER" (a) Find the number of 6 letter "words that can be formed by considering all possible permutations of the letters in the word "FATHER" (b) How many of these words begin with "F" and end with "R"? (c ) What is the probability of forming a six letter word that begins with F" and ends with "R" by randomly rearranging the letters in "FATHER?
1. Find expressions for each of the following. (Leave your answer as a mathematical expression rather than a number.) (a) The number of strings of 8 lower case letters (a-z) that do not contain any letter more than once. (b) The number of binary strings of length 10 that contain at most two Os. (c) The number of subsets of 11,2,,10 with three elements that contain at least one even number and at least one odd number. [Give brief justifications.]...
A letter is chosen uniformly at random from {A, B, . . . , Z}. If that letter is one of the vowels (i.e. A, E, I, O or U) then a second letter is chosen uniformly at random from {A, B, . . . , Z}. Let L be the number of letters chosen and let V be the number of vowels chosen. (i) What is the expected value of L? (ii) What is the expected value of V?...
4. Counting Problems. (a). Find number of ordered triples (x, y, z) of strictly positive integers such that 2 + y +z = 111. (b). Find the number of ways to arrange (all of) the letters of MATHEMATICS so that the result contains "EC" (so the letter E occurs immediately to the left of the letter C). (©). Find the number of ways to arrange (all of) the letters of MATHEMATICS so that the letter E occurs somewhere to the...
How many 6-letter code words can be formed from the letters T, O, U, DL, Y if no letter is repeated? If letters can be repeated? If adjacent letters must be different? There are possible 6-letter code words if no letter is repeated. (Type a whole number.) There are possible 6-letter code words if letters can be repeated. (Type a whole number) There are possible 6-letter code words if adjacent letters must be different. (Type a whole number.)
How many 8-letter words are there using the letters: A, B, C, D such that each letter is used exactly 2 times?
How many five letter words do not both begin and end with a vowel? (uppercase letters only)