As part of a quality-control program, 4 batteries from a box of 17 is chosen at random for testing. In how many ways can this test batch be chosen?

This test batch can be chosen in 2380 ways

Step-by-step explanation:

The order in which the batteries are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

In how many ways can this test batch be chosen?

4 batteries from a set of 17. So

This test batch can be chosen in 2380 ways

When we have a black dot in some value, means that the value is included in the set of solutions (associated with the signs ≤ ≥, and with solid lines)

When we have a white dot, means that the value is outside the set of solutions (associated with the signs < > and with dashed lines).

In this case, we can see the solid line across the solid point, but the dashed line does not cross over the white dot, this implies that the white dot belongs to the set of solutions (because is inside the shaded area) so this is an incongruence.

The dashed line should pass over the white dot.