Question

A certain lot consisting of ten items has three defective items and seven nondefective items. How many possible subsets of 2 items can be chosen from this lot?
21
45
90

Answer 1

Answer:

45

Step-by-step explanation:

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

Combinations formula:

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

$C_{n,x} = \frac{n!}{x!(n-x)!}$

How many possible subsets of 2 items can be chosen from this lot?

Combinations of 2 from a set of 10. So

$C_{10,2} = \frac{10!}{2!(10-2)!} = 45$