The number of ways in which n ties can be selected from a rack displaying 3n different ties, is

Let N denotes the number of ways in which 3n letters can be selected from 2n A's, 2nB's and 2nC's. then,

Let N denotes the number of ways in which 3n letters can be selected from 2n A's, 2nB's and 2nC's. then,

Number of ways in which three numbers in AP can be selected from 1,2,3, . .,n is

Number of ways in which three numbers in AP can be selected from 1,2,3, . .,n is

Given that n is odd, number of ways in which three numbers in AP can be selected from 1, 2, 3,……., n, is

Given that n is odd, number of ways in which three numbers in AP can be selected from 1, 2, 3,……., n, is

The number of ways in which 'n' different things can be arranged into 'r' different groups if blank groups are allowed is