## Task 4 - 070514

In the summer camp, a tent group is assigned by their pioneer leader to help in the kitchen with peeling potatoes. Three boys are to be selected from six for this task.

What is the number of all possible ways to form different groups?
The boys are denoted by $A, B, C, D, E, F$. From these, three are always to be selected, where for different groups, only the selected boys, but not the order of selection, are of importance.

By systematic approach, the following 20 groups are found:

| $A B C$ | $B C D$ | $C D E$ | $D E F$ | $A B D$ | $B C E$ | $C D F$ | $A B E$ | $B C F$ | $C E F$ |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| $A B F$ | $B D E$ | $A C D$ | $B D F$ | $A C E$ | $B E F$ | $A C F$ | $A D E$ | $A D F$ | $A E F$ |

Note: The number sought is equal to the combinations of 3 elements from a total of 6 elements.