Ten students attend a games night at which they will compete

Ten students attend a games night at which they will compete in teams of two. How many different collections of 5 such teams are there? This questions should be answered using the knowledge of sets, binary relations, functions, and by not using permutation combination formulas.

Solution

let each student be numbered as

s1 , s2 , s3, .............. s10

now they form team of two each

so

(s1, s2) one team

(s3, s4) seond team ....................... upto (s9, s10 ) fifth team

now each player can be mapped with 5 such teams.

and there are 10 such players,

now we an reframe our question as \" how many ways are there in which 10 players can be mapped with 5 teams, with each player must be mapped with atleast one team\"

1st player an be mapped with 5 team

2nd with 5 team ,,, 10 th player with 5 team

so total ways is 10* 5 = 50 ways