Combinations

[wanfango]

At my golf club we have 5 groups of 3 who play between 7 and 7.30 every Saturday. The club want to widen this window from 7.30 to 8.00 "to avoid the same people being drawn together" so often. This got me thinking as I think the problem is the computer is drawing effecticvly. So I challenged this assumption. For reference the "drawn" season at our club lasts for 24 weeks so I wanted to see how many weeks you could play with different combinations of players.

To calculate this I multiplied 15x14x13 to give 2730 combination of players. I then divided this by 15 (number of players per week) to get the answer to 182 weeks

If a season lasts 24 weeks then it would take over 7.5 seasons to have to play with the same 3 ball.

Have I missed something in the math here as 182 weeks seems really high number?

 

[Deleted member 4993]

At my golf club we have 5 groups of 3 who play between 7 and 7.30 every Saturday. The club want to widen this window from 7.30 to 8.00 "to avoid the same people being drawn together" so often. This got me thinking as I think the problem is the computer is drawing effecticvly. So I challenged this assumption. For reference the "drawn" season at our club lasts for 24 weeks so I wanted to see how many weeks you could play with different combinations of players.

To calculate this I multiplied 15x14x13 to give 2730 combination of players. I then divided this by 15 (number of players per week) to get the answer to 182 weeks

If a season lasts 24 weeks then it would take over 7.5 seasons to have to play with the same 3 ball.

Have I missed something in the math here as 182 weeks seems really high number?

If you choose 3 players at random from 15 players - then the number of ways to choose (or number of teams of 3):

\(\displaystyle _{15}C_{3} \, = \, \frac{15!}{3!\cdot (15-3)!} \, = \, 455 \, {teams} \, {of} \, {3}\)

5 teams play per week ? 91 weeks needed to complete