<span>65 = number of different arrangements of 2 and 3 card pages such that the total number of card slots equals 18.
416,154,290,872,320,000 = number of different ways of arranging 18 cards on the above 65 different arrangements of page sizes.
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This is a rather badly worded question in that some assumptions aren't mentioned. The assumptions being:
1. The card's are not interchangeable. So number of possible permutations of the 18 cards is 18!.
2. That all of the pages must be filled.
Since the least common multiple of 2 and 3 is 6, that means that 2 pages of 3 cards can only be interchanged with 3 pages of 2 cards. So with that said, we have the following configurations.
6x3 card pages. Only 1 possible configuration.
4x3 cards and 3x2 cards. These pages can be arranged in 7!/4!3! = 35 different ways.
2x3 cards and 6x2 cards. These pages can be arranged in 8!/2!6! = 28 ways
9x2 card pages. These can only be arranged in 1 way.
So the total number of possible pages and the orders in which that they can be arranged is 1+35+28+1 = 65 possible combinations.
Now for each of those 65 possible ways of placing 2 and 3 card pages such that the total number of card spaces is 18 has to be multiplied by the number of possible ways to arrange 18 cards which is 18! = 6402373705728000. So the total amount of arranging those cards is
6402373705728000 * 65 = 416,154,290,872,320,000</span>
Answer:
Step-by-step explanation:
Given
Required
Simpify
The very first step is to take LCM of the given expression
Perform arithmetic operations o the numerator
Divide the numerator and denominator by 2
The expression can't be further simplified;
Hence, =
Approximately 68% of a normal distribution lies within one standard deviation of the mean, so this corresponds to students with scores between (57.5 - 6.5, 57.5 + 6.5) = (51, 64)
45 + 0.35(45)
We can make it simpler:
1.35(45)
60.75
We can round up to 61
He needs about 16 more sales
Û = (-1, -1, -1)
^v = (2, 3, -5)
^v - û = (2 + 1, 3 + 1, -5 + 1) = (3, 4, -4)
Half way from ^v to ^(v - u) = ((3 - 2)/2, (4 - 3)/2, (-4 + 5)/2) = (1/2, 1/2, 1/2)
Halfway from û to ^v = ((2 + 1)/2, (3 + 1)/2, (-5 + 1)/2) = (3/2, 2, -2)
The required vector ^w = ((3/2 - 1/2), (2 - 1/2), (-2 - 1/2)) = (1, 1/2, -5/2)
