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 in

• A. $90$
• B. $45$
• C. $30$
• D. $60$

Answer 1

The correct option is A $90$

Total no. of persons $=6$

No. of ways to select 2 persons to form a pair$=C_1=(\frac{6}{2})$

No. of persons left after formation of first pair$=6-2=4$

No. of ways to form second pair from the remaining $4$ persons$=C_2=(\frac{4}{2})$

Total no. of games played$=C_1\times C_2$

$\Rightarrow \frac{6\times 5}{2}\times \frac{4\times 3}{2}$

$\Rightarrow 90$

Hence, answer is opion $A$