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Comment on Evening Out
Why can't we take this
stage 1: 4C1
stage 2: 5C1
stage 3: 3C1
and, then add these 3: 4+5+3= ?
IF it were the case that the
IF it were the case that the couple can do EXACTLY ONE activity then your approach would be correct. However, we're told that the couple does one OF EACH. So, for example, some possible evening plans include:
- Restaurant #1, Movie #4 and Teahouse #2
- Restaurant #2, Movie #1 and Teahouse #3
- Restaurant #3, Movie #2 and Teahouse #2
- Restaurant #2, Movie #2 and Teahouse #2
- Restaurant #3, Movie #1 and Teahouse #1
- Restaurant #4, Movie #5 and Teahouse #3
etc
Does that help?
Cheers,
Brent
Couldn't you break it into
Yes, we can also use
Yes, we can also use combinations for each stage.
However, since nC1 always equals n, we don't necessarily need to use combinations.
For example, there are 4 restaurants (call them A, B, C, and D).
So, we can select 1 restaurant in 4 ways (i.e., choose A or B or C or D)
Or we can use combinations (since the order in which we select 1 restaurant does not matter)
We can select 1 restaurant from 4 restaurants in 4C1 ways (= 4 ways)
We get the same results either way.
Cheers,
Brent