Question

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.

Answer 1

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

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

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:

`C=(n!)/((n-r))!r!) =(9!)/(2!7!)=(362880)/(2*5040)=36`

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:

`P=(n!)/((n-r)!)=(9!)/((9-7)!)=(362880)/(2)=181,440`