How many ways can the letters of the word CAPTION be arranged?

Answer 1

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!