<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.
=====
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:
7.56 km²
Step-by-step explanation:
Given data:
Width of the fjord, w = 6.3 km
Retreated terminus of the glacier between may 2001 and June 2005, d = 7.5 km
thus, the length lost , y = 7.5 - 6.3 = 1.2 km
now, the area is given as:
A = Length × width
on substituting the values, we get
A = 1.2 × 6.3
or
A = 7.56 km²
Hence, the surface area lost by the glacier in the fjord is 7.56 km²
<span>In this problem, we will use the combination
since the order does not matter but the flower can only be selected once. From the
given, we have a total of 11 flower and 9 flowerpots, to get the number of
possible combinations, we can write is at 11C9 or 11! / {9! (11-9)!}. The total
number of possible combinations is 55</span>
