First slide

Combinations

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

Moderate

A

90
B

45
C

30
D

60

Solution

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

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