Permutations an...

If $$\left( 2\le r\le n \right) $$, then $${ _{  }^{ n }{ C } }_{ r }+2{ _{  }^{ n }{ C } }_{ r+1 }+{ _{  }^{ n }{ C } }_{ r+2 }$$ is equal to

From a collection of $$20$$ consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

The number of selection of $$n$$ objects from $$2n$$ objects of which $$n$$ are identical and the rest are different is

The number of ways in which $$6$$ rings can be worn on the four fingers of one hand is

Ramesh number of ways in which the letters of the word RAMESH can be placed in the squares of the given figure so that no row remains empty, is  

Let n be the number of ways in which the letters of the word "RESONANCE" can be arranged so the vowels appear at the even places and m be the number of ways in which "RESONANCE" can arrange so that letters R,S,O,A appears in the order same as the word RESONANCE, then answers the following questions.
The value of n is 

For $$n$$ being natural number, if $$^{2n}C_r={}^{2n}C_{r+2}$$, find $$r$$.

The number of ways in which we can select 5 letters of the word INTERNATIONAL is equal to

How many different $$4$$-person committees can be chosen form the $$100$$ members of the Senate ?

If the letterss of the word 'NAAGI' are arranged as in a dictionary then the rank of the given word is