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How many ways can the letters of the word CAPTION be arranged?
Well, CAPTION is 7 letters, and you want to take all 7 of them and re-arrange them, and the order will matter, you will use the operation: nPr. The formula for this is: n!/(n-r)! In which the ! represents all the numbers counting down from the original number to 1. So if it was 5!, it would be 5 x 4 x 3 x 2 x 1= 120 The n is the number of items that you have, and the r is the number of items that you're taking. In CAPTION you have 7 letters, and you're taking 7 letters and re-arranging them in different ways, so it would be 7!/(7-7)!=5040 ways total!
How many ways can you arrange 4 out of 8 books on a shelf?
There are 8 ways to choose the first book There are 7 ways to choose the second book - 8 x 7 = 56 ways to select two books There are 6 ways to choose the third book - 8 x 7 x 6 = 336 way to select three books There are 5 ways to choose the fourth book - 8 x 7 x 6 x 5 = 1,680 ways to select four books.
How many ways can 7411111 be arranged?
The answer is 7!/5! = 42 ways.
In how many ways can 7 students line up a a ticket booth?
There are 5040 ways.
How many ways can 7 books be arranged vertically on a bookshelf?
If the books have to be the correct way up and spine outwards: 7! ways =7x6x5x4x3x2x1 =5040 ways. If the books can be any way in (upside down, spine inward, etc.): (7!x4^7) ways =7x4x6x4x5x4x4x4x3x4x2x4x1x4 =82,575,360 ways
