$^{n-1}C_3 + ^{n-1}C_4 > ^nC_3$,then the value of $n$ is

The number of ways that $8$ beads of different colours can be strung as a necklace is:

The sum of all three-digit numbers,formed using non-zero digits,where all the digits are perfect squares of a natural number,is:

For $2 \le r \le n$,the expression $\binom{n}{r} + 2\binom{n}{r-1} + \binom{n}{r-2}$ is equal to:

$A$ person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$,then $n$ equals

In an examination,Yamini has to select $4$ questions from each part. There are $6, 7,$ and $8$ questions in Part-$I,$ Part-$II,$ and Part-$III,$ respectively. What is the number of possible combinations in which she can choose the questions?