in how many ways can the numbers 1,2,3,4,5,6,7 be arranged so that  a. 1 and 7 are adjacent? b. 1 and 7 are not adjacent? c. 1 and 7 are exactly three spaces apart?

Q: Section: Name: 1. Write the following statement as an English sentence: "Em EZ, VnE Z, m = n +5" 2.…

A: Note- As per the honor code, only 3 sub-parts can be answered at a time. Please post other sub-parts…

Q: If [1 2 3 A = 3 -1 3] -1 0 2 23 1 of Find 2A - B stion Select one: a. none O b. -153 -5 6 0] O C.…

A: Solve the matrix

Q: 6. Let A= {1,3,5), B = {2,4,6,8), C={2,3,4,5) Which of the following statements is false? A. An B=0…

A: We have to check which of the following statements is false.

Q: Classify each of the following statements as true or false. If false, tell why. 5 is a divisor of…

A: We need to classify each of the following statements as true or false. If false, tell why. 1.5 is a…

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: 00 Points P and Q are plotted on the number line. P. + 0. + -8 -6 -4 -2 4 6. Which expression…

A: If p and q are plotted on a number line (the line is in one dimension) Then distance between p and…

Q: How many different line arrangement could be made with the SYMBOLS given below O a. 7!/(3!) O b.…

A:

Q: Which of the following are disjoint sets?* O D. (1,3,5) and (2,4,6) B. (1,2,3) and (2,3,4) O c.…

A:

Q: * 00 2N IFN=(1,2,3,4,..), C= {x |x = 2n- 1, n E N), D= (x |x = 2n, nE N), and ( = {x |x=2n +1, n=0…

A:

Q: Suppose that S and T are points on the number line , ST = 17 and S lies at 4, where could be located…

A:

Q: Disprove the following statements. (a) If n and m are natural numbers, then nm is composite. (b) For…

A: I have given an answer in step 2.

Q: 4. For P -1, (4 + i) ? 15 + 8i 15 + 4i 16 + 4i 16 + 8i CLEAR ALL

A:

Q: How many integers in the set {1,2, ..., 10°} are divisible by 495 and not by 75?

A:

Q: 2. (CLO3) In how many different ways can we arrange the letters HOOKAAHUAAA so that the two O's are…

A: Word: HOOKAAHUAAA

Q: Three cards are randomly selected, without replacement, from an ordinary deck of 52 cards. Compute…

A: According to the provided information, the card are randomly selected, without replacement from an…

Q: From a point 4 miles north of a cell tower, a hiker walks 2.5 miles west. How far is the hiker from…

A: Let us first make a diagram to understand the problem better. The hiker is initially at A, 4 miles…

Q: The mode of the numbers 1,1, 2, 3, 4, 5, 5, 5, 6, 6,6, 6 is a. None of these b.6 c 5 d.1

A: Mode:  Most frequently occurred value. Given data: 1,1, 2, 3, 4, 5, 5, 5, 6, 6,6, 6 here 1-occurs 2…

Q: Write the value of each Fibonacci number of the following nth terms. You may use Binet's formula. 4.…

A:

Q: If |A|  8 and |B|  5, what is |A ∪ B| + |A ∩ B| ?

A:

Q: Which of the following sets are equal? A. {2,3} × {3, 4} B. {3, 4} × {2,3} C. {2, 2, 3, 3} × {3, 3,…

A: To choose: The sets which are equal. A. 2,3×3,4 Find the set. 2,3×3,4=2,3,2,4,3,3,3,4 B. 3,4×2,3…

Q: If d is g(a, b) and c is another natural number which also divides both a and b. Then c also divides…

A: Given that c divides a and b ,d belongs to( a ,b) so assume a,b are 4,8 and c is 2 and d is 6

Q: a. |15| b. |15| +4 c. 3- | 17| d. |12|+|12|

A:

Q: 4. Which number line best shows the location of √√7? A. 2 3 ++++> 3 +++* ++++++>

A: Locate 7 on number line

Q: Given A={x,y},B={1,2,3,} and C={m,n}. How many ordered pairs are there for AXBXC

A: Elements of A×B are the ordered pairs of the form  A×B=x, y | x∈A, y∈B Given : A=x, y, B=1, 2, 3,…

Q: 10. Given A= a. |AB| b. |ATA| c. |5A| d. |A-¹B| e. BAT| -3 8 0 1 and B = 32 2 4 1 find:

A:

Q: Assume a, b and c are real numbers greater than 1. Find p, q and r so that the following equality…

A:

Q: iv C = {1,2, 3} v How many elements are in the powerset of N = {1,2, 3,... ,n} for some n E N?

A:

Q: If+b+=++, then show that for 1 a" +b" +c"

A:

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.