Six ‘$+$’ and four ‘$-$’ signs are to placed in a straight line so that no two ‘$-$’ signs come together, then the total number of ways are

From a class of $25$ students, $10$ are to be chosen for an excursion party. There are $3$ students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these

four cards belong to four different suits,

Ten persons, amongst whom are $A, B$ and $C$ to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is

A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to

In a club election the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote be $62,$ then the number of candidates is :-