You are going to the store to get 14 cans of soda. There are 5 varieties...

You are going to the store to get 14 cans of soda. There are 5 varieties to choose from, and you are to bring back at least 1 of each variety. How many different assortments can you choose to come back with?

Expert Solution

Here we have to choose from 5 varieties such that atleast one of each variety is present while choosing 14 cans of soda. Consider that you have already selected 5 cans of each variety and there are 9 more cans that you have to choose now. Now we need to find how these rest of 9 cans should be distributed.

For this, consider the sticks and dots scenario.

In this figure consider the sticks(|) to be the rest of 9 cans which have to be distributed. The dots(*) represent the number of cans belonging to specific variety. In the above example there are 2 cans of first variety , 0 cans of secnd variety , 4 cans of third variety, 2 cans of 4th variety and 1 can of 5th variety. The example we have given is a specific case. We need to find how many of these cases exist. This will simply be the ways of selecting 4 places out of 13 places for dots(*). Hence the number of different assortments would be given by,

N = C(13,4) = 715

orchestra answered 2 years ago

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