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How many ways can 4 DVDs be arranged on a shelf?
Solution:
There are 4 ways to choose the first DVD, 3 ways to choose the second, 2 ways to choose the third and 1 way to choose the last. In other words, there are 4 x 3 x 2 x 1 = 4! =24 ways to arrange the DVDs.
Example: How many ways can John, Katherine, Luke, Melanie and Nick sit at a table?
Solution: The number of ways to arrange these five people is 5!
5! = 5 x 4 x 3 x 2 x 1 = 120. There are 120 permutations.
Example: How many ways can n objects be arranged?
Solution: n objects can be arranged in n! ways.
Example of Probability: Example: By using a die, what is the probability of rolling two 3s in a row? Solution: From the previous example, there is a 1/6 chance of
Consider the regression model Y i = a + bX i + u i , where the X i are non-stochastic and the u i are independently and identically distributed with E[u i ] = 0 and va
how can i easily solve the trignometry question?
How many square centimeters are in one square meter? There are 100 cm in a meter. A square meter is 100 cm through 100 cm. The area of this is 10,000 sq cm (100 × 100 = 10,000)
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L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers [7] 2.2 In a given day he will
The Cartesian product (also called as the cross product) of two sets A and B, shown by AΧB (in the similar order) is the set of all ordered pairs (x, y) such that x€A and y€B. What
Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ut(x, 0) = ?(x) =1 if-1 Sketch snapshots of the solution u(x, t) at t = 0, 1, 2 with justification (Hint: Sket
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