Permutations an...

If $${ S }_{ n }={ C }_{ 0 }{ C }_{ 1 }+{ C }_{ 1 }{ C }_{ 2 }+.......+{ C }_{ n-1 }{ C }_{ n }$$ and $$\frac { { S }_{ n+1 } }{ { S }_{ n } } =\frac { 15 }{ 4 } $$, then value of n

If $$x+y=1$$, then $$\displaystyle\sum^n_{r=0}r\cdot {^{n}C_r}x^r\cdot y^{n-r}=?$$

The number of ways of 3 scholarship of unequal value be awarded to 17 candidates, Such that no candidate gets more than one scholarship is 

The number of permutations of letters of the word "PARALLAL" atken four at a time must be, 

The value of $$\sum _{ r=0 }^{ s }{ \sum _{ s=1 }^{ n }{  }  } ^nC_s.$$ $$^sC_r$$ (where $$r\le s$$ is )

There are n identical red balls & m identical green balls. The number of different linear arrangements consisting of "n red balls but not necessarily all the green balls" is $${^{x}C_y}$$ then?

The exponent of 11 in $$^{200}C_{125}$$ is 

$$1+1.1!+2.2!+3.3!+...+n.n!$$ is equal to 

If $$\displaystyle \frac{1}{{^4{C_n}}} = \frac{1}{{^5{C_n}}} + \frac{1}{{^6{C_n}}}$$, then $$n=$$

The number of such numbers which are even (all digits are different) is