n! (п — 2)!

Q: 2. c. How many arrangements are there of the letters of the word CHEESECAKE under each condition?…

A: In CHEESECAKE , there are total 10 letters with E repeated 4 times, and C repeated 2 times . As E…

Q: n 21. if an+1 = an an 2n + 3 n=1

A: We have, an+1=n2n+3an Substitute value of n=0,1,2,3,4,..... At n=0, a1=020+3a0a1=0 At n=1,…

Q: 1UT) 117 If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next…

A: We have to prove the given expression using the given information of arithmetic progression.

Q: 12 Find the term of (a – 3b)" that has b in it.

A:

Q: If an = V5n – 5, list the first five terms of an, starting with n = 1: {a1, a2, a3, a4, a5}

A:

Q: 11 If A (n)= 7n-23, what is the value of a,? Your Answer

A:

Q: If ~q is TRUE, then what will be the output of ~p -> ~q Select one: TRUE ~p q p

A: Statement p→q is true if q is true or both p, q are false As it is given that ~q is TRUE. So, ~p→~q…

Q: b. The location of 0.47 is between which two hash marks on the number line? and Which of these two…

A: The location of 0.47 is between two hash marks on the number lies 0.4 and 0.5. The 0.47 closet to…

Q: How many 12-digit numbers have all their digits in nondecreasing order? For example, 266888 is a…

A: Let the twelve digits be d1,d2,d3, d4,d5,d6,d7,d8,d9,d10,d11,d12 from left to right. Let a1=d1…

Q: • Suppose repetitions are not permitted. (a) Find the number of three-digit numbers that can be…

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

Q: (a) Find the value of P(?, 4) and P(?, 6) using permutation formula, where ? is 31

A: To Find the value of (?, 4) and (?, 6) using permutation formula, where ? is 31.

Q: と 4. BDC ~ A ABC hint each time you get stuck ♡ 2. Reach nnt

A:

Q: How many 4-digit numbers have all their digits in nondecreasing order? For example, 266888 is a…

A: Solution:- In the given problem, we will find how many 4-digits number have all their digits in…

Q: A binomial has two terms. O True O False

A:

Q: In n 22. n=2 _n² 8

A: Given: ∑n=2∞ln(n)n2

Q: 6.) Derike the binomial idendity nent) (un-) C Hint: For mzz, c^)+2(^) +m?]

A: To derive the binomial identity22+42+62+.........+2n2=nn+14n-16

Q: If m|n then lcm(m,n) = n. :Select one True False

A: Given m|n Hence n=am , where a is some integer Therefore nis a multiple of m

Q: n² < 2" for n = 4, 5, 6, ... (Hint: 2n + 1 < 2" for n= 3,4,5, ...)

A:

Q: (a) Find the value of P(?, 4) and P(?, 6) using permutation formula, where ? is 39

A: The permutation formula is defined as follows:

Q: 2" is O(n²) True False False. This was the correct answer.

A: Given statement is 2n is On2

Q: * if the o is not known and (n< 30) can be used z O

A: Which one is the correct choice

Q: (e) Show that every n ≥ 8 can be written as 3a+5b for some a, b € N.

A: Part e asked and answered.

Q: Write the following expression without using the factorial symbol (n-4)!/(n-1).    A.…

A: Known fact: n!=1×2×3×…×n-1×n

Q: Show combination notation in solving the problem below. A box contain 6 distinct red balls and 4…

A:

Q: n² < 2" for n = 4,5, 6, ... (Hint: 2n + 1 < 2" for n = 3,4, 5, ...)

A:

Q: (10)5n n! 17 Select one: True False

A: Find true or false

Q: If A =P-BP then B=Q-lAQ for o-1=P- True False

A:

Q: Evaluate the factorial or permutation. P(n,0) Choose the correct answer below. O A. n! О в. о Ос. 1…

A:

Q: How many permutations of the letters ABCDEFGHIJ contain ) the string EF? D the strings BCA and FGH?…

A: Use the given information.

Q: . n &gt; 5 only if n &gt; 7.

A: Given that n&gt;5 only if n&gt;7

Q: 2" Q# lo n! n=1

A: From the given problem:   2nn!n=1∞   So we can also write as, ∑n=1∞2nn!=201!+212!+223!+⋯   As we…

Q: (b) Give two different interpretations of the bino- mial coefficient (") for non-negative integers n…

A: First we will give two different interpretations of the binomial coefficient nk for non-negative…

Q: Find :18th term of the A.P. 2, 3/2, 5/2.

A:

Q: Suppose that 56 % of students play football, 53 % of students play cricket, and 12 % of students…

A: Let F=students play footballC=students play cricketGiven,P(F)=0.56P(C)=0.53P(F¯∩C¯)=0.12

Q: I am trying to figure out how to make a know-show table for the question If m is an even integer,…

A: We can make a know-show table for the given condition.If m is an even integer, then the expression…

Q: Use the 'Permutations' formula to evaluate the expression P(29, 3).

A: Given that the expression: P (29, 3) The permutation formula is given by, Pn,r=Prn=n!n-r!…

Q: . What is the probability of getting a blue or white ball if there are 50 balls in total, where 23…

A: According to our guidelines, we can answer only three sub-parts. So, please repost the rest parts.

Q: Which of the following is the sum of all four-digit numbers that can be formed by the digits 1, 3,…

A: The given digits are 1,3,5,7,9 We know sum of r digits number = n-1Pr-1 Sum of all n digits number…

Q: If 3rd and 9th term of an A.P. are 4 and -8 respectively

A:

Q: 20 n 27 = loo64tnl00/31

A: In this question, some logarithmic property is applied. logab=logbloga logab=bloga

Q: If m|n then lcm(m, n) = n. :Select one True False

A: True

Q: Find the value of p(x,4)and p(x,6) using permutation formula where x is the 09.

A: We have to find the value of p(x, 4) and p(x, 6) using the permutation formula. Here, x=09

Q: Write out the expression Tk (n=4) in full. Which are free and which are dummy indices? Jki 2,

A:

Q: Simplify the permutation.P(n,1)

A: Formula to be used - P(n, r) = n!n-r!

Q: Find the next two terms in (an)n20 beginning

A: Given,             3,  5, 11, 21, 43, 85, . . .

Q: Determine the "n" and "p" in the following problems and write them in Combination notation. a)Abag…

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

Q: ined by - N = 0 will be

A:

Q: nd her brother has 8 visitors. In how many ways can they be seated including Clara and her brother…

A: Carla has = 6 visitors Her brother has = 8 visitors we have to find  how many ways can they be…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.