The question addresses finding different basketball lineups from a roster of 12 athletes by utilizing permutation concepts, resulting in 95,040 possible lineups.
Permutations involve the arrangement of objects in a specific order. In this case, the basketball coach selecting different lineups from 12 athletes requires finding the number of permutations possible.
To calculate this, you use the formula for permutations: P(n,r) = n! / (n - r)!. Substituting n = 12 (number of athletes) and r = 5 (number of players in a lineup), the number of different basketball lineups the coach can play is 95,040.
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