Learning Materials
Features
Discover
Chapter 1: Q5E (page 41)
Prove that Following no. is an Integer
\(\frac{{4155 \times 4156 \times ....4250 \times 4251}}{{2 \times 3 \times .... \times 96 \times 97}}\)
The given no \(\frac{{4155 \times 4156 \times ....4250 \times 4251}}{{2 \times 3 \times .... \times 96 \times 97}}\) is an integer.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Letnandkbe positive integers such that bothnandn鈭�kare large. Use Stirling鈥檚 formula to write as simple an approximation as you can forPn,k.
If two balanced dice are rolled, what is the probability that the difference between the two numbers that appear will be less than 3?
Suppose that 40 percent of the students in a large population are freshmen, 30 percent are sophomores, 20 percent are juniors, and 10 percent are seniors .Suppose that10 students are selected at random from the population, and let X1, X2, X3, X4 denote, respectively, the numbers of freshmen, sophomores, juniors, and seniors that are obtained.
a. Determine 蟻(Xi, Xj ) for each pair of values i and j (i< j ).
b. For what values of i and j (i<j ) is 蟻(Xi, Xj ) most negative?
c. For what values of i and j (i<j ) is 蟻(Xi, Xj ) closest to 0?
If two balanced dice are rolled, what is the probabilitythat the sum of the two numbers that appear will be even?
Three six-sided dice are rolled. The six sides of each die are numbered\(1 - 6\). Let A be the event that the first die shows an even number, let B be the event that the second die shows an even number, and let C be the event that the third die shows an even number. Also, for each\(i = 1,2,...,6\), let\({A_i}\)be the event that the first die shows the number i, let \({B_i}\) be the event that the second die shows the number i, and let \({C_i}\)be the event that the third die shows the number i. Express each of the following events in terms of the named events described above:
a. The event that all three dice show even numbers
b. The event that no die shows an even number
c. The event that at least one die shows an odd number
d. The event that at most two dice show odd numbers
e. The event that the sum of the three dices is no greater than 5.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine