Given:
- 5 clarinet players
- 3 flute players
- 2 saxophone players
Total number of players = 5 clarinet players + 3 flute players + 2 saxophone players = 10 players
To form a duet of clarinet players, we need to select 2 players from the 5 clarinet players.
The number of ways to select 2 clarinet players from 5 is given by the combination formula:
Number of ways = 5 choose 2 = 5! / (2! * (5-2)!) = (5 * 4) / (2 * 1) = 10
So, there are 10 possible duets consisting of all clarinet players.
Now, the total number of possible duets that can be formed by selecting any 2 players from the 10 players is given by the combination formula:
Total possible duets = 10 choose 2 = 10! / (2! * (10-2)!) = (10 * 9) / (2 * 1) = 45
Therefore, the probability of selecting a duet consisting of all clarinet players is:
Probability = Number of clarinet duets / Total possible duets = 10 / 45 = 2 / 9
So, the probability of selecting a duet consisting of all clarinet players is 2/9.
