Ou are assembling a loft. One piece of wood has 9 screw holes in a straight row, but you can only find 7 screws (which look identical). In a hurry, you put the 7 screws in the 9 holes. If exactly 7 holes are selected, how many outcomes are in the sample space when: (1) the order of selection does not matter. (2) the order of selection matters.

1) If the order doesn't matter, there are 36 possible outcomes.

2) If the order does matter, there are 181,440 possible outcomes.

Step-by-step explanation:

1) In the case when the order doesn't matter , we have to calculate a combination of 7 screws in 9 holes.

We use the formula for combinations:

being r: the number of screws and n: the number of holes.

2) When the order does matter, the possible outcomes are called permutations. We have permutations of 7 screws in 9 holes.

We use the formula for permutations: