There are n numbered seats around a round table. Total number of ways in which n1(n1

Question

There are n numbered seats around a round table. Total number of ways in which n1(n1< n) persons can sit around the round table, is equal to (A)  n Cn1 (B)  n pn1 (C)  n Cn1-1 (D)  n pn-1

Tardigrade Admin · Accepted Answer

When seats are numbered, circular permutation is same as linear permutation as seat number is also important. Thus, total number of sitting arrangement = n pn1

Q. There are $n$ numbered seats around a round table. Total number of ways in which $n_{1} (n_{1} < n)$ persons can sit around the round table, is equal to

$^{n} C_{n_{1}}$

$^{n} p_{n_{1}}$

$^{n} C_{n_{1} - 1}$

$^{n} p_{n - 1}$

When seats are numbered, circular permutation is same as linear permutation as seat number is also important. Thus, total number of sitting arrangement $=^{n} p_{n_{1}}$

Q. There are n numbered seats around a round table. Total number of ways in which n1​(n1​<n) persons can sit around the round table, is equal to

nCn1​​

npn1​​

nCn1​−1​

npn−1​