If $^{n + 1}{C_3} = 2{\,^n}{C_2},$ then $n =$

In how many ways can five examination papers be arranged so that physics and chemistry papers never come together?

The number of integers greater than $6000$ that can be formed using the digits $3, 5, 6, 7,$ and $8$ without repetition is:

Out of $18$ points in a plane,no three are in the same straight line except five points which are collinear. The number of $(i)$ straight lines,$(ii)$ triangles which can be formed by joining them is

If ${}^n{P_5} = 20 \cdot {}^n{P_3}$,then $n = $

In how many ways can $6$ letters be posted in $5$ letter boxes available in the locality?