Suppose 4 fair coins are tossed. Use pascals triangle to find a number of ways of obtaining exactly 3 heads

Q: How many unique codes are possibly formed from three parts, where the first part can be A to E, the…

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Q: 3. Find the number of distinct permutations that can be formed your ID number.

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Q: 2) Each type of machine part made in a factory is stamped with a code of the form…

A: We can use :- 26 letters, 10 digits, 10 digits (as digits can be repeated)   Total number of…

Q: In how maAny ways can Five s budents be Seabed in arow thab has 10 chairs

A: Given, n = 10 X =5 This  is the case f permuatation.       To  find, In how many ways can 5 students…

Q: Two-digit natural numbers are formed, with replacement, from the digits 0 through 9. How many…

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Q: 2. Use Pascal's triangle given in Table 9.7.1 to compute the values of а. b. С.

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: How many different six-digit codes can be formed using digits 0 through 9? What counting technique…

A: Given set of digits A= {0,1,2,3,4,5,6,7,8,9} Total number of digits = 10 we have to find six- digit…

Q: How many different numbers which contain from thr an be formed from the digits A, B, C, D and E. and…

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Q: ms in row #14 of the Pascal’s triangle

A: In this question, the concept of the pascal triangle is applied. Pascal Triangle Pascal's Triangle…

Q: in pascals triangle which row has a sum of 65536?

A: We know that the sum of every row of Pascal's triangle is twice of the last row's sum.  And it is…

Q: 3find gformyle for the nith daran of the falowlhw sepuences 1625- to

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Q: 1. How many 3 or 4 digit even numbers greater than 700 can be formed by: a. Using the digits 0-9.…

A: Let there are three chairs A, B and C in one side of a table. The different ways in which these…

Q: What will be the sum of numbers in the 16th row of Pascal’s triangle ?

A: Please refer the attached image for complete solution.

Q: What is the largest number in the row starting "1 4 ..." of Pascal's triangle?   What is the sum…

A: To find what is the largest number in the row starting "1 4 ..." of Pascal's triangle? To find what…

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: How many unique codes are possibly formed from two characters, where the first character can be 2 to…

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Q: How many unique codes are possibly formed from three parts, where the first part can be A to C, the…

A: The above problem exhibits an example of an ordered arrangement, as the order the objects are…

Q: How many different words with or without meaning can be formed with the letters of the word…

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Q: In how many way can we arrange the letters of the world DIGIT O NONE O 1260 O 60 O 30 O 24 O 120

A: Given, DIGIT  words are  D -> 1  I -> 2 G -> 1 T -> 1

Q: 3. Consider the word PERMUTE and all the ways you can arrange its letter using each letter only once…

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Q: What is the 4th term in the n = 8 row of Pascal's Triangle?

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Q: How many unique codes are possibly formed from three parts, where the first part can be A to D, the…

A: There are some useful technique in determining the number of different ways of arranging or…

Q: Assuming that any arrangement of letters forms a 'word', how many 'words' of any length can be…

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Q: In how many distinct ways can a 18-digit number be made using nine 9's and nine 9's?

A: We have to find the distinct ways a 18-digit number be made using nine 9's and nine 9's.

Q: What mistakes are found in this proof.

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Q: Use Pascal's Triangle to expand (5 + 2y)*.

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Q: How many unique codes are possibly formed from two characters, where the first character can be 3 to…

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Q: A computer system allows user IDs that are six characters long. If only alphanumeric characters are…

A: We have a computer system that allows user IDs which are six characters long,And, there is only…

Q: What is the sum of the first 6 terms in Diagonal 5 of the Pascal's Triangle?

A: First draw the Pascal's triangle. The starting diagonal is called as diagonal 0 .

Q: 1.A club with 15 members will choose 3 of them to attend a meeting. In how many different ways can…

A: Given that there are total 15 members and we will choose 3 of them. Since we will pick 3 persons in…

Q: How many unique codes are possibly formed from three parts, where the first part can be A to E, the…

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Q: Give 5 math patterns found in Pascal's triangle

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Q: Write down the 7th row of Pascal's Triangle.

A: We have to find the 7th row of Pascal's Triangle

Q: Find the 10th term in the 15th row of Pascal's triangle.

A: We will find out the required term .

Q: A combination lock opens with the correct 5 digit code. Each wheel rotates through the digits 1 to…

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Q: how many six-digit numbers can be formed so that 2 are in the place of thousandth and 5 in the place…

A: First number can not be 0. So we can pick the first number in 9 ways. (1 to 9)

Q: how many perfect numbers are there between 1,000,000 and 9,000,000

A: Given- The numbers between 1,000,000 and 9,000,000. To find- The perfect square number between the…

Q: Write the first four terms in row #17 of Pascal’s Triangle?

A: Pascal's Triangle is

Q: Use Pascal's Triangle to expand (1+2y)ª. (1+ 2y)*

A: Remember how the Pascal triangle work

Q: Use Pascal's triangle to expand the expression. (4x + 1)4

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Q: How many unique codes are possibly formed from three parts, where the first part can be A to C, the…

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Q: How many four-digit even numbers are possible if the leftmost digit cannot be zero? Repitition is…

A: The possible total ten numbers are {0,1,2,3,4,5,6,7,8,9}.Since the left most digit cannot be zero,…

Q: What is the value of the smallest composite number with exactly 3 distinct prime num- ber in its…

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Q: How many different heptominoes (made from 7 squares) are there that have 5 squares in a column and 1…

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Q: How many 5-number license plates can be made using the digits 1,2,3,4,5,6,7, if an odd digit must…

A: Given Data: The total number of digits available is: n=7 The numbers required on number plate is:…

Q: 2) Find the number of distinguishable permutations of the digits of the number 911 912 271. 3) In…

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Q: 11 How many 6-letter words (even without meaning) can be created from the letters of the word…

A: There are several powerful methods for counting objects and sets of objects without actually having…

Q: What is the sum of the first 7 terms in diagonal 10 of the Pascal’s triangle?

A: Given :   Pascal's triangle

Q: How many unique codes are possibly formed from three parts, where the first part can be C to E, the…

A: As we have got three parts and there are various elements in these parts which we can use to make a…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.