If a die is rolled 35 times, there are 635 different sequences possible. The following question asks how many of these sequences satisfy certain conditions.  What fraction of these sequences have exactly five 1s? (Round your answer to four decimal places.)

Q: How many four letter sequences are possible that use the letter a,b,c and d once each. ????

A: We have four different letters a, b, c and d. Our aim is to find the number of all possible…

Q: Three men and three women are to be seated in a row of chairs numbered 1 through 6. (a) How many…

A: When n people are arranged in a line it can be arranged by n!

Q: Use permutations to solve. From a cooler with 6 different kinds of soda, 4 are selected for 4…

A: nPr = n!/(n-r)!

Q: Consider the following digits: 0, 1, 2, 3, 4, 5, and 6. if a three-digit number is to be formed and…

A:

Q: Three men and three women are to be seated in a row of chairs numbered 1 through 6. (a) How many…

A: Given   Three men and three women are to be seated in a row of chairs numbered 1 through 6.

Q: A, B, C, D, or F at the end of the semester. (a) What is the minimum number of students required in…

A: From extended Pigeonhole Principle we know that if there is n pigeon and m pigeon holesn>m then…

Q: The 5th term of an A.P. is 15 and the first term is 3. What is the sum of the first 10 terms?

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Q: A penny collection contains twelve 1967 pennies, seven 1968 pennies, and eleven 1971 pennies. If you…

A: Generalized pigeonhole principle For any function f form a finite set X with n elements to a finte…

Q: At a certain university there are 19 different time periods during which classes can be scheduled.…

A: Given that, in a certain university, there are 19 different time periods during which classes can be…

Q: In how many ways can 6 different cupcakes be arranged in a circular stand?

A: The number of ways n items can be arranged in a circle is equal to n-1!. The formula for n! is…

Q: sub: discrete How many ways can a group of five people be selected from nine people?

A: There are total 9 people. To Find: Number of ways that we can select a group of five people from…

Q: For how many n ∈ {1, 2, 3, …, 1000} is n a multiple of one or more of 5, 6, or 7?

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Q: The Reverend minister of a church always insist that every member shake hands with every other…

A: Given: Number of person is, n=90. Number of times required handshake is 1 time. The objective is…

Q: If a die is rolled 40 times, there are 640 different sequences possible. The following question asks…

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Q: For how many n Ee {1,2, ..., 550} is n a multiple of one or more of 9, 4, or 7?

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Q: a. Exactly 24 of them survive their first year of life. b. At most 25 of them survive their first…

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Q: A is now 34 years old, and B is 4 years old. In how many years will A betwice as old as B?

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Q: In how many ways can we select 7 books out of 9 and arrange them on a bookshelf? a. 181,440 b. 72 c.…

A: we have to find In how many ways can we select 7 books out of 9 and arrange them on a bookshelf.

Q: The freshman basketball team has ten players. Only five can play on the court atone time. How many…

A: Given problem:- The freshman basketball team has ten players.Only five can play on the court atone…

Q: What fraction of these sequences have exactly three 3s and three 2s?

A: Think of a sequence as thirty empty slots. We want to 10 slots to contain 3’s and 2’s of which we…

Q: A ternary digit is either 0, 1, or 2. How many sequences of nine ternary digits are possible…

A: The ternary digit is either 0 or 1 or 2.

Q: Which of the following should replace the question mark to complete the series?* 日日日 O Option 4…

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Q: What is the missing number (as indicated by the blank line) and the 12th number in the series? 1, 1,…

A: Given that the series 1,1,2,3,5,8,13_,34,55,...

Q: If the die above is rolled 120 times, predict the number of times it would land on a multiple of 3.…

A: It is an important part of statistics . It is widely used .

Q: How many prime numbers are there between 200 and 210?  a. none  b. three  c. one  d. two

A: numbers between 200 and 210 are  201, 202,203,204,205,206,207,208 and 209 Prime number are the…

Q: n a party there are 38 guests who shook hands with exactly one another once. How many handshakes…

A: Given: Number of guests = 38 Number of people required for a handshake = 2

Q: A jar contains four blue marbles numbered one to four. The jar also contains four red marbles…

A: Blue marble :{1,2,3,4} : total 4 Red marble :{1,2,3,4} : total 4

Q: For how many n € {1, 2, . . ., 550} is n a multiple of one or more of 5, 4, or 6?

A: We know that x is used to denote the greatest integer less than or equal to x. For example: 2.5 is…

Q: A ternary digit is either outcomes 2. How many sequences of ten ternary digits are possible…

A: Given ternary digit is either 0, 1, or 2. sequences of ten ternary digits are possible containing a…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.