For a game in which two partners play against two other partners, six persons are available. If every possible pair must play with every other possible pair, then the total number of games played is

Question

For a game in which two partners play against two other partners, six persons are available. If every possible pair must play with every other possible pair, then the total number of games played is (A) 90 (B) 45 (C) 30 (D) 60

Tardigrade Admin · Accepted Answer

For one game four persons are required.
This can be done in

^{6} C_{4} = 15

ways.
Once a set of

4

persons are selected, number of games possible will be

\frac{^{4} C _{2}}{2} = 3

games.

∴

Total number of possible games

= 3 \times 15 = 45

.

Q. For a game in which two partners play against two other partners, six persons are available. If every possible pair must play with every other possible pair, then the total number of games played is

$90$

$45$

$30$

$60$

For one game four persons are required.
This can be done in $^{6} C_{4} = 15$ ways.
Once a set of $4$ persons are selected, number of games possible will be $\frac{^{4} C _{2}}{2} = 3$ games.
$∴$ Total number of possible games
$= 3 \times 15 = 45$ .