Question

A person wishes to make up as many different parties as he can out of 20 friends with the condition that each party consists of the same number. How many should he invite at a time?

• A. 5
  
• B. 10
  
• C. 15
  
• D. 20

Answer 1

The correct option is B

10

Since, n = 20 is even, ${20}_{C_r}$ is greatest when $r=\frac{20}{2}=10$.
Hence, the maximum number of parties ${20}_{C_{10}}$.
Thus he should invite 10 friends at a time in order to form the maximum number of parties.