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it is 12! or 479,001,600.
421.001.600
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In how many ways can 12 books be displayed in 12 books are available?
12! = 12x11x10x9x8x7x6x5x4x3x2x1 = do the math yourself. Explanation: The first books has 12 options, the second book has 11, the third book has 10, et cetera.
How many ways can a group of 12 including 4 boys and 8 girls be formed into two 6 person volleyball teams with no restrictions?
462 waysExplanationIn the question, it does not seem to matter how many boys or girls are on a team. So really you are asking how many ways are there to divide 12 people into two teams of 6.The answer is (12C6)/2 where 12C6 means 12 choose 6First 12 chose 6 is 12!/(12-6)!(6)! which is 12x11x10x9x8x7x6x5x4x3x2x1/(6x5x4x3x2x1)(6x5x4x3x2x1)=(12x11x10x9x8x7)/(6x5x4x3x2x1)=924(As a side note, the Google browser will calculate these numbers if you just type in 12 choose 6, for example)Now once one team of 6 is chosen, the other team is automatically the remaining 6 so we have really double counted. That is why we divide by 2 and the answeris 462 ways.
What math is used when solving a rubik's cube?
MATHEMATICS OF THE CUBE The center pieces of each face are always in the same relationship to each other. Therefore, the number of ways the other pieces can be arranged in relation to them (ie the possible arrangements of the cube) is: Total possible arrangements = (possible arrangements of Corner Pieces) x (possible arrangements of Edge Pieces). Possible Arrangements of Corner Pieces: There are 8 Corner Pieces. Therefore, the possible different arrangements of them is 8! (ie 8x7x6x5x4x3x2x1) = 40320. Each Corner Piece has three different orientations, so this must then be multiplied by 3 to the power 8 (ie 3x3x3x3x3x3x3x3) which equals 6561. However, with the actual cube, once the second from last Corner Piece is placed, the last piece can have only one automatic orientation so this should be divided by 3 (effectively 3 to the power 7) which equals 2187. Thus, total possible arrangements of Corner Pieces = 40320 x 2187 = 88,179,840. Possible Arrangements of Edge Pieces: There are 12 Edge Pieces. Therefore, the possible different arrangements of them is 12! (ie: 12x11x10x9x8x7x6x5x4x3x2x1) = 479,001,600. However, with the actual Cube (and unlike Corner Pieces) it is impossible to exchange just two Edge Pieces, so once the third from last is placed, the remaining two can have only one possible arrangement, so this total must be divided by 2, which equals 239,500,800. Each Edge Piece has two different orientations, so this must then be multiplied by 2 to the power 12 (ie 2x2x2x2x2x2x2x2x2x2x2x2) which equals 6561. However, with the actual cube, once the third from last Edge Piece is placed, although the last two pieces will be in fixed positions, one can be reoriented but the last will always have a fixed orientation in relation to it. So this must be divided by 2 (effectively 2 to the power 11) which equals 2048. Thus, total possible arrangements of Edge Pieces = 239,500,800 x 2048 = 490,497,638,400. So - Total Possible Arrangements of Rubik's Cube = (possible arrangements of Corner Pieces) x (possible arrangements of Edge Pieces) = 88,179,840 x 490,497,638,400 = 43,252,003,274,489,856,000. Roughly speaking, 4.3 times 10 to the power 19. in simple yes, because it uses several mathematical algorithms.
