A swimming instructor is making the lane assignment for the five participants in the upcoming competition. There are five lanes available. Each swimmer is to be assigned to one lane and each lane is to be used by one swimmer. The lanes are labeled 1-5. Let L represent the set of lanes: L = {1, 2, 3, 4, 5} and P represent the set of participants: P = {Amy, Briana, Carla, Dalia, Elyse}. How many assignments are possible if in each assignment Briana must be assigned to to an odd-numbered lane and Elyse must be assigned to an odd-numbered lane ?

Question

A swimming instructor is making the lane assignment for the five participants  in the upcoming competition. There are five lanes available. Each swimmer is to be assigned to  one lane and each lane is to be used by one swimmer. The lanes are labeled 1-5.  Let L represent the set of lanes: L = {1, 2, 3, 4, 5}  and P represent the set of participants: P = {Amy, Briana, Carla, Dalia, Elyse}.  How many assignments are possible if in each assignment Briana must be assigned to  to an odd-numbered lane and Elyse must be assigned to an odd-numbered lane ?

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Identify Constraints: Identify the constraints for the lane assignments. Briana and Elyse must be assigned to odd-numbered lanes. There are three odd-numbered lanes available: 1, 3, and 5.Assign Odd-Numbered Lanes: Assign Briana and Elyse to the odd-numbered lanes. There are 3 odd-numbered lanes and 2 swimmers (Briana and Elyse) who must be assigned to these lanes. We can assign Briana to any of the 3 lanes, and then Elyse to any of the remaining 2 lanes. Number of ways to assign Briana and Elyse = 3 × 2 = 6 ways.Assign Remaining Swimmers: Assign the remaining swimmers to the remaining lanes. After assigning Briana and Elyse, there are 3 participants (Amy, Carla, Dalia) and 3 lanes left (one odd-numbered and two even-numbered). We can assign these participants to the remaining lanes in 3! (3 factorial) ways. 3! = 3 × 2 × 1 = 6 ways.Calculate Total Assignments: Calculate the total number of possible assignments. The total number of assignments is the product of the number of ways to assign Briana and Elyse and the number of ways to assign the remaining participants. Total number of assignments = 6 (from Step 2) × 6 (from Step 3) = 36 ways.

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