Permutations an...

A vehicle registration number consists of $$2$$ letters of English alphabet followed by $$4$$ digits, where the first digit is not zero. Then, the total number of vehicles with distinct registration numbers is

If $$\displaystyle ^{ 16 }{ C }_{ r }=^{ 16 }{ C }_{ r+1 }$$, then the value of $$\displaystyle ^{ r }{ P }_{ r-3 }$$ is
$$\displaystyle $$

If $$X, Y, Z, D, E$$ and $$F$$ are $$6$$ distinct points on the circumference of a circle, find the number of different chords which can be drawn using any $$2$$ of the $$6$$ points.

If $$_{  }^{ n }{ { P }_{ r } }=30240$$ and $$_{  }^{ n }{ { C }_{ r } }=252$$, then the ordered pair $$\left( n,r \right) $$ is equal to

The value of $$\dfrac {(n + 2)! - (n + 1)!}{n!} $$ is:

If $$^{n}C_{12} = ^{n}C_{6}$$, then $$^{n}C_{2}$$is equal to:

$$^n C_{r-1}\, =\, 330,\, ^nC_r\, =\, 462,\, ^nC_{r+1}\, =\, 462\, \Rightarrow\, r\, =$$

If $$a=99^{50}+100^{50}$$ and $$b=101^{50}$$, then :

If n is an integer with $$0\le n \le 11$$ then the minimum value of $$n!(11-n)!$$ is attained when a value of n = 

The number of words that can be formed out of the letters of the word "ARTICLE" so that the vowels occupy even places is