SOLUTION: In how many ways can a selection of at most five desserts be made from a dessert trolley containing 6 desserts

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Question 1137755: In how many ways can a selection of at most five desserts be made from a dessert trolley containing 6 desserts
Answer by ikleyn(52909) About Me  (Show Source):
You can put this solution on YOUR website!
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You can select either 0 of 6, or 1 of 6, or 2 of 6, or 3 of 6, or 4 of 6, or 5 of 6 by 


    C%5B6%5D%5E0 + C%5B6%5D%5E1 + C%5B6%5D%5E2 + C%5B6%5D%5E3 + C%5B6%5D%5E4 + C%5B6%5D%5E5 ways.


Taking into account that


    C%5B6%5D%5E0 + C%5B6%5D%5E1 + C%5B6%5D%5E2 + C%5B6%5D%5E3 + C%5B6%5D%5E4 + C%5B6%5D%5E5 + C%5B6%5D%5E6 = 2%5E6 = 64,


the answer to the problem's question is 


    C%5B6%5D%5E0 + C%5B6%5D%5E1 + C%5B6%5D%5E2 + C%5B6%5D%5E3 + C%5B6%5D%5E4 + C%5B6%5D%5E5 = 2%5E6 - C%5B6%5D%5E6 = 64 - 1 = 63.


ANSWER.  In 63 ways.