A probability problem by shreyas shastry
Probability
Level
3
In a bakery four types of sweets are available.In how many ways a person can buy 10 sweets if he decide to take at least one sweets of each variety ?
The answer is 84.
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First put one sweet of each type in your shopping basket. You now need to choose six more in any combination of the four types.
Imagine lining up these sweets on the counter, with a "divider" between different types to keep them separate. So, for example, getting 4 of type A, 2 of type C and none of types B or D would look like this:
O O O O | | O O |
If you always place them in order, your set of possible configurations is isomorphic to the set of possible choices of where to put the dividers.
And of course there are 9C3 ways to place those dividers, which equals 84.