If a die is rolled 30 times, there are 630 different sequences possible. The following question asks how many of these sequences satisfy certain conditions.  What fraction of these sequences have exactly eight 1s and eight 6s? (Round your answer to five decimal places.)

Q: How many arrangements begin with the letter M from math power

A: The total number of letters in MATHPOWER is 9 letters.  It is given that the first letter has to be…

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: 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: 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: The first figure of the Sierpinski triangle has one shaded triangle. The second figure of the…

A: First figure contains one shaded triangle, second figure contains 3 shaded triangles, third figure…

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: How many even 4-digit numbers can be formed from the digits 1, 2, 6, 7, and 9 with no repetitions…

A: There is no repetition allowed.. At unit place we have two choices 2 or 6 In 10th place we have…

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: 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 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: For how many n = {1, 2, ..., 695} is n a multiple of one a multiple of one or more of 8, 3, or 7?

A: In the range of [1, 695] the number of numbers divisible by an integer k =  represents the floor…

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: For how many n = {1, 2,…, 645} is n a multiple of one or more of 8, 7, or 3?

A: n belongs to (1,2,....645) is n a multiple of one or more of 8,7 or 3.

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: is company and every year he adds 7 cars, then how many cars will he own in 8 years? O 161 O 311 O…

A: We are given, Initial cars=16Number of cars added per year=7 Hence, the number of cars after 8…

Q: Suppose a dice is thrown and a coin is then tossed. How many different outcomes are there if the…

A: Fundamental counting principle: If an event can occur in m ways and an other independent even can…

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…

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.