Dean, Gabrielle, and Kevin, who all work at the same large company, have received the 'Employee of the Month' award this month. As a result, their names will be published in the company newsletter. In how many different orders could they be listed in the newsletter?
orders
There are 3 people, so we can start with 3 choices for the first spot. After one person is listed, there are only 2 left for the second spot, and then only 1 left for the last spot. Therefore, the total number of different orders they could be listed in is:
3 x 2 x 1 = 6
So there are 6 different orders they could be listed in the newsletter.
the answer to A florist is working on a wedding bouquet that uses 5 different types of flowers. In how many different orders can the various types of flowers be added to the bouquet?
orders
There are 5 different types of flowers to add to the bouquet. We can start with 5 choices for the first flower to add, then 4 choices for the second, 3 choices for the third, 2 choices for the fourth, and 1 choice for the last. Therefore, the total number of different orders the flowers could be added to the bouquet is:
5 x 4 x 3 x 2 x 1 = 120
So there are 120 different orders the flowers could be added to the bouquet.
To determine the number of different orders the names can be listed in the newsletter, we can use the concept of permutations. The formula for permutations of n objects taken r at a time is given by:
P(n, r) = n! / (n - r)!
In this case, there are 3 names (Dean, Gabrielle, and Kevin) that need to be listed, which means n = 3. We need to list all 3 names, so r = 3. Plugging these values into the formula, we get:
P(3, 3) = 3! / (3 - 3)!
= 3! / 0!
= 3! / 1
= 3
Therefore, there are 3 different orders in which the names could be listed in the newsletter.