Seven chairs, $A$ to $G,$ are arranged as shown. In how many ways can the chairs be occupied by $7$ of a group of $12$ people if three particular people are asked to sit on chairs $B,D$ and $F,$ in any order?

 

A minibus has $11$ passenger seats. There are six seats in a row on the sunny side and five seats in a row on the shady side, as shown in the following diagram.

Find how many ways eight passengers can be arranged in these seats if:

there are no restrictions

A minibus has $11$ passenger seats. There are six seats in a row on the sunny side and five seats in a row on the shady side, as shown in the following diagram.

Find how many ways eight passengers can be arranged in these seats if:

one particular passenger refuses to sit on the sunny side

A minibus has $11$ passenger seats. There are six seats in a row on the sunny side and five seats in a row on the shady side, as shown in the following diagram.

Find how many ways eight passengers can be arranged in these seats if:

two particular passengers refuse to sit in seats that are either next to each other or one directly in front of the other.

Find the number of ways in which five apples can be selected from:

eight apples

Find the number of ways in which five apples can be selected from:

nine apples and $12$ oranges.

From seven men and eight women, find how many ways there are to select:

four men and five women

From seven men and eight women, find how many ways there are to select:

three men and six women

From seven men and eight women, find how many ways there are to select:

 at least $13$ people.