Final answer:
Nicole can choose her two nicknames from her current four nicknames in 6 different ways according to the combination formula. The possible pairs of nicknames are Tricky & Nicky, Tricky & Coyote, Tricky & Slim, Nicky & Coyote, Nicky & Slim, and Coyote & Slim.
Step-by-step explanation:
The question involves combinatorics, a topic in mathematics, specifically the calculation of combinations. Nicole needs to reduce her number of nicknames from four to two.
To determine all her choices, we use the combination formula to find the number of ways to select 2 nicknames out of 4, which is C(4, 2).
The formula for combinations is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.
Applying the formula, we get: C(4, 2) = 4! / (2! * (4 - 2)!)
= (4 * 3) / (2 * 1)
= 6.
Hence, Nicole has 6 different ways to choose 2 nicknames from her current 4. The possible combinations are:
- Tricky and Nicky
- Tricky and Coyote
- Tricky and Slim
- Nicky and Coyote
- Nicky and Slim
- Coyote and Slim