Out of 3n given things 2n are alike and the rest are different Show thata selection of 2n things can be madde from these 3n things in `2^(n)` different ways .

There are 4n things of which n are alike and the rest different. Find the number of permutations of 4n things taken 2n at a time, each permutation containing the n like things.

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

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

Number of ways of selecting one or more things out of n dissimilar things are

Number of ways of selecting r consecutive things out of n things

Number of ways of selecting one or more things out of n dissimilar things are

Number of ways of selecting one or more things out of n dissimilar things are

If the number of arrangements of (n-1) things taken from n different things is k xx the number of arrangements of (n-1) things taken from n things in which two things are identical then the value of k is