Permutations an...

 $$\left( ^ { 2 n } C _ { 0 } \right) ^ { 2 } - \left( ^ { 2 n } C _ { 1 } \right) ^ { 2 } + \left( ^ { 2 n } C _ { 2 } \right) ^ { 2 } - \ldots + ( - 1 ) ^ { 2 n } \left( ^ { 2 n } C _ { 2 n } \right) ^ { 2 }$$  equals to

If $${C_r} = {\,^n}{C_r}\,\,and\,\,\left( {{C_0} + {C_1}} \right)\,\,\left( {{C_1} + {C_2}} \right)......$$
$$\left( {{C_{n - 1}} + {C_n}} \right) = k\frac{{{{\left( {n + 1} \right)}^n}}}{{n!}}$$ then the value of k is 

If $$^{35}C_{n+7}=^{35}C_{4n-2}$$, then the value of $$n$$ is

In a conference hall 10  executive are to be seated on 10 chairs placed left to right. Executive $$E_1$$ wants to sit to the right of $$E_2$$ Also, $$E_4$$ wants to sit the left of $$E_1$$ and $$E_5$$ wants to sits to the left of ways $$E_4$$ Number of ways the executives can be seated on the 10 chairs, is 

Total number of four-digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are

What is the hundreds digits of ( 20 !-15!) ? 

If $$n$$ and $$r$$ are positive integers such that $$r < n$$ then $$^{n}C_{r}+^{n}C_{r-1}$$ is equal to

The number of five digit numbers in which digits decrease from left to  right, is 

If $$x\epsilon N and C^{x-1_{4}}-C^{X-1}_{3}-\frac{5}{4}P^{x-2}_{2}< 0$$ then x is equal to 

If  $$m$$  and  $$n$$  are positive integers more than or equal to  $$2 , m > n ,$$  then  $$( m n ) !$$  is divisible by