Rhea has 10 basketballs each of a different colour. She only has time to shoot 5 hoops before going to bed.How many different arrangements can the balls be thrown into the hoops? 1 120 square 2 square 3 30,24 o

Here's how to solve this problem:<br /><br />**Understanding the Problem**<br /><br />Rhea is choosing 5 basketballs out of 10, and the order in which she shoots them matters (since the question asks about *arrangements*). This is a permutation problem.<br /><br />**Formula**<br /><br />The formula for permutations is:<br /><br />P(n, r) = n! / (n - r)!<br /><br />Where:<br /><br />* n = total number of items (10 basketballs)<br />* r = number of items being chosen (5 basketballs)<br /><br />**Calculation**<br /><br />P(10, 5) = 10! / (10 - 5)!<br /> = 10! / 5!<br /> = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1)<br /> = 10 * 9 * 8 * 7 * 6<br /> = 30,240<br /><br />**Answer**<br /><br />The correct answer is 30,240. So, option 3 is correct.<br />