Question

Five books are chosen from a group of ten and put on a bookshelf. How many permutation (order matters) possible arrangements are there?

Answer 1

To calculate the number of possible arrangements when 5 books are chosen from a group of 10, we use the formula for permutations.

Step-by-step explanation:

To calculate the number of possible arrangements when 5 books are chosen from a group of 10, we can use the concept of permutations. In this case, order matters, so we can use the formula for permutations: nPr = n!/(n-r)!. Here, n represents the total number of items (10 books) and r represents the number of items being chosen (5 books). Plugging in the values, we get 10P5 = (10!)/(10-5)! = (10!)/(5!).

Using factorials, 10! = 10x9x8x7x6 = 30,240 and 5! = 5x4x3x2x1 = 120. So, 10P5 = 30,240/120 = 252. Therefore, there are 252 possible arrangements when 5 books are chosen from a group of 10.