math word problem

Question

Shawn has decided to start his own tennis tournament with fifteen players. In round one each player must play a match with every player in the tournament. How many matches will there be in round one? Explaining in words and One Rule of your choice to explain the answer.

Please help me with this word problem.

Answer 1

how many combinations of 2 players are there if there are 15 players altogether ?

15!/2!(15-2)!

15!/2!13!

(15*14)/2=15*7=105 matches

or,...

the first player plays with each of the 14 other players for a total of 14 matches

the second player plays with each of the 13 other players (he already played with the first player) for a total of 13 matches

the third player plays with each of the 12 other players

the fourth player plays with each of the 11 other players

do you see a pattern ?

add the matches together

14+13+12+11+10+9+8+7+6+5+4+3+2+1=105