Person wishes to make up as many different parties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite are ..A.... . Here, A refers to

Question

Person wishes to make up as many different parties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite are ..A.... . Here, A refers to (A) 8 (B) 9 (C) 10 (D) None of these

Tardigrade Admin · Accepted Answer

Suppose he invites r friends at a time. Then, number of parties = 20 Cr And we know n Cr is maximum for r=(n/2), when n is even. Hence, he should invites 10 friends at a time, in order to have maximum parties.

Q. Person wishes to make up as many different parties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite are ..A.... . Here, A refers to

8

9

10

None of these

Suppose he invites $r$ friends at a time.
Then, number of parties $=^{20} C_{r}$
And we know $^{n} C_{r}$ is maximum for $r = \frac{n}{2}$ , when $n$ is even.
Hence, he should invites 10 friends at a time, in order to have maximum parties.

Q. Person wishes to make up as many different parties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite are ..A.... . Here, A refers to

8

9

10

None of these

Suppose he invites r friends at a time. Then, number of parties =20Cr​ And we know nCr​ is maximum for r=2n​, when n is even. Hence, he should invites 10 friends at a time, in order to have maximum parties.

Suppose he invites $r$ friends at a time.
Then, number of parties $=^{20} C_{r}$
And we know $^{n} C_{r}$ is maximum for $r = \frac{n}{2}$ , when $n$ is even.
Hence, he should invites 10 friends at a time, in order to have maximum parties.