Six '$+$' and four '$-$' signs are to be placed in a straight line so that no two '$-$' signs come together. Then,the total number of ways is:

In how many ways can $15$ different books be divided equally among $5$ sets or groups?

The total number of $4$-digit numbers which can be formed using the digits $1, 2, 3, 4$ without repetition such that the digit $n+1$ never immediately follows the digit $n$ (for $n=1, 2, 3$) is:

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

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?

$A$ candidate is required to answer $6$ out of $10$ questions,which are divided into two groups each containing $5$ questions. The candidate is not permitted to attempt more than $4$ questions from each group. In how many ways can the candidate make their choice?