Can someone explain when you have a P&C problem that has multiple sets within the problem when do you multiply the sets together to get the answer and when do you add the sets to get the answer?
Examples:
1) The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also, assume that each bin can hold one and only one blend)
2) A pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. In how many different arrangements can the dolphins swim?
With the first question you add 4!/(2!2!) + 4!/3! + 4!/4!
With the second question you multiply 3! * 3!
In general, how can you tell when you would add vs when you would multiply the sets?
Thanks in advance.
Examples:
1) The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also, assume that each bin can hold one and only one blend)
2) A pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. In how many different arrangements can the dolphins swim?
With the first question you add 4!/(2!2!) + 4!/3! + 4!/4!
With the second question you multiply 3! * 3!
In general, how can you tell when you would add vs when you would multiply the sets?
Thanks in advance.
