The total number of different combinations of one or more letters which can be made from the letters of the word '$MISSISSIPPI$' is

Six '$X$'s have to be placed in the squares of the figure such that each row contains at least one '$X$'. In how many different ways can this be done?

Out of $5$ apples,$10$ mangoes,and $15$ oranges,$15$ fruits are to be distributed between two persons. Find the total number of ways of distribution.

For a scholarship,at most $n$ candidates out of $2n+1$ can be selected. If the number of different ways of selecting at least one candidate for the scholarship is $63$,then the maximum number of candidates that can be selected for the scholarship is -

The number of ways in which $5$ male and $2$ female members of a committee can be seated around a round table so that the two female are not seated together is

Out of $6$ boys and $4$ girls,a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys?