Q9--------------Arjit being party animal wants to hold .................?

Question

Q9--------------Arjit being party animal wants to hold as many partes among 20 frnds.However his father has warned him that he will be finanancing his parties under following conditions.
-----The inviteis have to be among his 20 best frnnd.
----------He can’t call the same st of frnds to party more than once.
------------The number of invitees to ever party have to be same.

Given these constraints,Arjit wants to hold maximum number of parties.How many frnds should he invite to eac party.
a. 11
b. 8
c. 10
d. 12

Answer 1

If the number of friends at each party is k, the number of different possible sets of friends is 20Ck. You should know that the combination function nCr has a maximum for a particular value of n when r = n/2, so in this case the maximum number of combinations (and hence of possible parties) will be when 20/2 = 10 friends are invited to each party.

You can verify this by working out values:
20C8 = 125,970
20C9 = 167,960
20C10 = 184,756
20C11 = 167,960
20C12 = 125,970

Answer 2

8