Francesca is picking out material for her new quilt. At the fabric store, there are 17
solids, 7
striped prints, and 9
floral prints that she can choose from. If she needs 2
solids, 3
floral prints, and 4
striped fabrics for her quilt, how many different ways can she choose the materials?
To find the total number of ways Francesca can choose the materials for her quilt, we will multiply the number of options for each type of fabric:
Number of ways to choose 2 solids: 17 choose 2 = 17! / [(17-2)! * 2!] = 136
Number of ways to choose 3 floral prints: 9 choose 3 = 9! / [(9-3)! * 3!] = 84
Number of ways to choose 4 striped fabrics: 7 choose 4 = 7! / [(7-4)! * 4!] = 35
Total number of ways to choose the materials = 136 * 84 * 35 = 405,360
Therefore, Francesca can choose the materials for her quilt in 405,360 different ways.