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Answer :
Final answer:
The probability of selecting five eastern conference representatives and six western conference representatives for the NHL players' labor negotiation committee is approximately 29.84%.
Explanation:
To find the probability of selecting five eastern conference representatives and six western conference representatives for the NHL players' labor negotiation committee, we need to use the concept of combinations. The total number of ways to select a committee of 5 representatives from 6 players in the eastern conference is given by the combination formula C(6,5) = 6. Similarly, the total number of ways to select a committee of 6 representatives from 12 players in the western conference is given by the combination formula C(12,6) = 924. The total number of ways to choose 5 representatives from the eastern conference and 6 representatives from the western conference is the product of these two combinations, which is 6 * 924 = 5,544. The total number of possible committees is the combination of all player representatives, which is C(6+12, 5+6) = C(18, 11) = 18,564. Therefore, the probability of selecting five eastern conference representatives and six western conference representatives is 5,544 / 18,564 ≈ 0.2984, or approximately 29.84%.
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