One cold, snowy winter evening on Valentine’s Day, Jasper was in a hurry to buy a bouquet for his sweetheart Molly while rushing on the way to her birthday party.
The only flower shop Jasper found open among the swirling snow flurries was the Thrifty Flower Emporium, where a total of fifteen flowers were left, namely five Lily of the Incas, four anemones, three carnations and three daffodils.
Since Jasper didn’t have much money on him, he decided to buy just three flowers, one for each of the years he had known Molly.
However, there was the problem of choosing the right combination of flowers, which caused a mental block to occur in Jasper, and he stepped from one foot to the other in complete indecision.
The shop attendant, Susan, noticed Jasper’s panicky bewilderment, and informed him that they had just bought a Smart Pick flower randomizer which could select from among the available flowers and have Jasper’s bouquet for Molly ready in a jiffy.
This good news put a big smile on Jasper’s face, and in no time Jasper walked out of the Thrifty Flower Emporium proudly exhibiting a bouquet with three flowers in his hand, in a sprint to reach Molly’s birthday party on time.
What would you say were the number of possible triple-flower bouquets that could be made with the fifteen flowers available at the Thrifty Flower Emporium?
And what is the probability that all the flowers were different?