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: 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: * 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…

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

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

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

A: Locate 7 on number line

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:

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

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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?

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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.