Permutations an...

$$^{60}C_{60}=?$$

If $$^{n}C_{18}={^nC_{12}}$$, then $$^{32}C_n=?$$

There are $$10$$ points in a plane, out of which $$4$$ points are collinear. The number of triangles formed with vertices as these point is?

When simplified, the expression 
$$^{ 47 }{ C }_{ 4 }+\sum _{ j=1 }^{ 5 }$$   $$^{ 52-j }{ C }_{ 3 } $$ equals to

How many $$3$$-digit numbers are there?

If $$^{ n }{ C }_{ r-1 }=10,$$ $$^{ n }{ C }_{ r }=45,$$ and $$^{ n }{ C }_{ r+1 }=120,$$ then r equals

In an examination, a candidate has to pass in each of the five subjects. In how many ways can he fail?

A committee of $$5$$ is to be formed out of $$6$$ gents and $$4$$ ladies. In how many ways can this be done when each committee may have at the most $$2$$ ladies?

Out of $$7$$ consonants and $$4$$ vowels, how many words of $$3$$ consonants and $$2$$ vowels can be formed?

In how many ways can a committee of $$5$$ members be selected from $$6$$ men and $$5$$ ladies, consisting of $$3$$ men and $$2$$ ladies?