topic: counting  How many strings of five capital letters are there... a. if no letter can be repeated? b. if the string starts with G and letters can be repeated? c. if the string ends with A and letters cannot be repeated

Q: How many different 5-letter words can be made a. if the first letter must be C, Z, T, or L and no…

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Q: . Let n =12,612,6x0,725,725 . a. If 9 | n, then x = ________ . b. If 11| n, then x = ________.

A: (a) We know 9 | n iff the sum of the digits of n is divisible by 9.     n = 126126x0725725    =>…

Q: In how many ways can a president, vice president, secretary, and treasurer be elected from a group…

A: Step 1:Here is group of 6 people.From this, we need to choose 4 people: president , Vice president ,…

Q: There are 58 runners in a race. How many ways can the runners finish first, second, and third? There…

A: From the given information, total number of runners = 58. The objective is to find the number of…

Q: p.e. 3. Identify a pattern in each list of numbers. Then use this pattern to find the next number.…

A: Let x be the missing number.

Q: A pet store surveyed 603 people to see how many own a cat, how many own a bird, and how many own a…

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Q: Identify a pattern in the given list of numbers. Then use this pattern to find the next number.…

A: Given that the series 55 , 52 , 49 , 46 , 43 , ____

Q: There are 15 finalists in a singing competition. The top four singers receive prizes. How many ways…

A: Given data, Number of finalists in a singing competition n=15  The top four singers receive prizes.…

Q: A student is given a reading list of eight books from which he must select three for an outside…

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Q: o Digits = {0, 1, 2, ...,9} o Letters = {A, B, C,..., X, Y, Z} %3D o How many valid passwords are…

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Q: Use permutations to solve. The student activity club at the college has 39 members. In how many…

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