Mathematics, 18.07.2019 16:30 rosieanneanney

Roberto wants to display his 18 sports cards in an album. some pages hold 2 cards and others hold 3 cards. how many different way can roberto display his figures?

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There are 65 different page arrangements that will have 18 card slots. Total possible arrangements taking into consideration the 65 different page orders is 65 * 18! or approximately 4.16154x10^17 The least common multiple of 2 and 3 is 6. And 18 divided by 6 is 3. So you'll have 3 sets of pages and each set of pages will be either 2 pages of 3 cards or 3 pages of 2 cards. So they are (3,0) = 6 pages of 3 cards. (2,1) = 4 pages of 3 cards, 3 pages of 2 cards. (1,2) = 2 pages of 3 cards, 6 pages of 2 cards. (0,3) = 9 pages of 2 cards. For each of the 4 different combinations of pages, there are multiple ways of arranging them. They are 6 pages of 3 cards, has only 1 possible arrangement. 4 pages of 3 cards, 3 pages of 2 cards, has 7!/(4!3!) = 35 2 pages of 3 cards, 6 pages of 2 cards, has 8!/(2!6!) = 28 9 pages of 2 cards, has 1 possible arrangement. So the number of different ways to have 2 card and 3 card pages is 1 + 35 + 28 + 1 = 65 different arrangements. And finally for each of the 65 different page arrangements, there are 18! different ways to order the cards to place on those pages. To demonstrate, for the first card, you can select any of the 18 cards. The second card can be any of the 17 remaining cards, the third card can be any of the 16 remaining cards, and so on. For a total of 18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 different ways to order the 18 cards. Multiply that by the 65 different page arrangements and you have 65*18! different possible arrangements.

Answer from: Quest

Xis -1/2
y is 35/4.
18x-9y=-18 12x+8y=64 what does x equal and what does y equal?

Answer from: Quest

answer:

total cost for tiles and paints is $924.

step-by-step explanation:

we have been given that a community hall is in the shape of a cuboid. the hall is 40m long 15m high and 3m wide.

the paint will be required for 4 walls and ceiling.

let us find area of walls and ceiling.

$\text{area of walls and ceiling}=(2*40*15)+(2*3*15)+(40*3)$

$\text{area of walls and ceiling}=1200+90+120$

$\text{area of walls and ceiling}=1410$

therefore, the area of walls and ceiling is 1410 square meters.

given: cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter. therefore,

$\text{ the total painting cost}=10*(\frac{1410}{25})$

$\text{ the total painting cost}=10*56.4=564$

therefore, the total painting cost is $564.

tiles will be required for floor. let us find the area of floor.

$\text{area of floor} = 40*3\text{ square meters}$

$\text{area of floor} =120\text{ square meters}$

given: 1m squared floor tiles costs $3. so,

$\text{total cost for tiles} = 3*120 = 360$

therefore, the total tiles cost is $360.

now let us find combined total cost of tiles and paint.

$\text{combined total cost}= 564+360 = 924$

therefore, the combined total cost of tiles and paint is $924.

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