Permutations an...

Kathy is scheduling the first four periods of her school day. She needs to fill those periods with calculus, art, literature, and physics, and each of these courses is offered during each of the first four periods. Calculate the total number of different schedules Kathy can choose from.

If $$^{(n-1)}C_3+^{(n-1)}C_4 > ^nC_3$$, then the minimum value of $$n$$ is:

In how many different orders can five boys stand on a line?

Six points were chosen on a circle and every possible chord was drawn. Two chords, which do not have the common points are named separately. How many pairs of separate chords exist in the situation described above?

Let $$\boxed { n }$$ be defined as $$\frac{(n+2)!}{(n-1)!}$$, what is the value of $$\frac{\boxed{7}}{\boxed {3}}$$ ?

If $$^6P_r = 360$$ and $$^6C_r =15$$,then find $$r?$$

The total number of five digit numbers the sum of whose digits is odd is 

Find the coefficient of the middle term of the expansion $$\left (x-\dfrac{1}{2y}\right)^{10}$$:

A company has $$5$$ men and $$6$$ women. What are the number of ways of selecting a group of eight persons?

The value of $${ }^{10}C_1 +{ }^{10}C_2 + { }^{10}C_3 + ... + { }^{10}C_9$$ is