Question

Pool cues a pair of pool players have 4 different cues, and every day, they pick two random cues and play snooker for an hour. in the last year, they have played together a total of 210 hours. interestingly, their random picking of cues has worked so well that each cue has been used the same number of hours. how many hours has each cue been used?

Answer 1

Using combinations and assuming uniform distribution, each of the 4 cues has been used for 105 hours over the last year.

Step-by-step explanation:

To solve this question, we use the concept of combinations and uniform distribution. There are 4 cues and the players each day pick 2. The total number of ways to pick 2 cues from 4 is calculated using combinations, which is represented as 4C2 (or "4 choose 2"). This results in 4C2 = (4!)/(2!*(4-2)!) = 6 different combinations. Because each of the 4 cues has been used for the same number of hours, we can assume uniform distribution of usage across all cues.

Since there are 210 hours of play in total and each combination of cues has been used an equal number of times, each combination has been used for 210 hours / 6 combinations = 35 hours. In each combination, 2 cues are used, so each individual cue is used for 35 hours * 3 combinations = 105 hours.

Thus, each cue has been used for 105 hours over the last year.