Answer :
Final answer:
To calculate the number of ways a volleyball coach can choose 8 players from a group of 12, we use the mathematics concept of combinations. By applying the formula, the coach has 495 possible combinations of players for the first game.
Explanation:
The scenario you're asking about relates to a concept in mathematics called combinations, which deals with how many ways you can select a subset from a larger set, order not being important. To calculate the number of ways the volleyball coach can select 8 players from a group of 12, we can use the formula for combinations, which is nCr = n! / [r!(n-r)!], where 'n' is the total number of elements, 'r' is the elements to be chosen, 'nCr' is the number of combinations, and '!' denotes factorial. Here, n=12 (total players), and r=8 (number to be chosen). Substituting the values into the combination formula, the total number of ways the coach can choose is given by 12C8 = 12! / [8!(12-8)!]. Upon computation, the number of ways the coach can choose is 495.
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