Let denote the binomial coefficient (also written as C(n, r) or nCr). The sum of (C) + (4) + (5)+.+(12) ... is O 1,728 O 1,024 O 4,096 O 2,048

Q: A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. How…

A: Given that 5 types hard candies  Cherry, Strawberry, Orange, Lemon, Pineapple We have to find number…

Q: Which of the following real number would be the coefficient of x in the binomial expansion of

A: Using binomial expansion formula find that there is no term of x in the binomial expansion of the…

Q: (n+1)! (n-1)! = 10n

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Q: Explain why the Binomial Theorem can be stated as

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Q: (QuestionID:T1Q2.4) What is the coefficient of 2° in the binomial expansion of (2² – 1)5 ? Choose…

A: What is the coefficient of x3 in the binomial expansion of (x2-1)5

Q: Expand 3x + 2y)7 using the binomial theorem. Simplify your final result.

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Q: (1+ 2x + 4x? +8x + ...)(3x² + 3x* + 3a° + · . .)(x³ + 2a® + 3x° +

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Q: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

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Q: Some casinos use 5 standard 52-card decks mixed together into one big deck (calleda superdeck ). So,…

A: In some casinos, multiple standard 52-card decks are combined to form what is known as a superdeck.…

Q: What is the “binomial coefficient of (11/7)? calculate. show how.

A: Given information- We have given- (11/7) = C711 We have to find the binomial coefficients.

Q: 1. Use the binomial theorem to expand (a) (1+x)* and (b) (1+x). 2. Use the binomial theorem to…

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Q: 10. Use the binomial theorem to evaluate (2r³ - y) 5.

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Q: Compute the following (a) C6, 2 (b) C7, 7

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Q: . Expand the binomial (2x - 1)*.

A: Binomial theorem

Q: Write down the expansion of : 4 1 3x 2 by the binomial theorem.

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Q: In the expansion of (x + y)16 which term has the same coefficient as x14y2? O a. x12,4 Oc x3y14 O d.…

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Q: Wht is the sum of this 8.1 - 3.1 x 2.1 + 0.4

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Q: Use the binomial theorem (more than once) to expand (a+b+c)³.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 19. Determine the binomial power that when expanded is x12 x⁹ + x6 x15 + x3 1 + Show your work. 2 16…

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Q: Evaluate the given binomial coefficient

A: Binomial coefficient: It is denoted by Ckn=nk=n!k!(n-k)!

Q: If the sum 5+ 5(3)+5(3)² +...+5(9)* =5465 then the value of k is (a) 5 (b) 6 (c) 3 (d) 4

A: We know that 1+a+a2+a3+…+an-1=an-1a-1, if a≠1

Q: 12. Use the Binomial Theorem to expand the expression (2x-3y). Show your work.

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Q: Prove the following using the binomial theorem: ()=()+ 2n

A: In this context, the aim is to prove 2n2=2n2+n2.

Q: Use the binomial theorem to expand the expression (u - 5v)¹

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Q: um 1+4+7+..

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Q: What is the coefficient of x4y2z6 in the expansion of (3x² + 2y + 3z3)6?

A: Apply binomial theorem and isolate the coefficient

Q: The probability that an archer hits the target is p = 0.9, so the probability that he misses the…

A: Here's it follows binomial distribution with trial 6 and probability of success 0.9 , probability of…

Q: (2x-3y) =

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Q: 3. What is the highest power of 13 that will divide 9000! without leaving a remainder? (a) 749 (b)…

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