Can someone help me with these questions? 1. A municipal election has four candi

Question

Can someone help me with these questions?

1. A municipal election has four candidates: Abe Adams, Betty Bryant, Chuck Cameron, and Donna Davis. If 5000 citizens cast votes, how many different ways could the votes be dis- tributed among the candidates? 2. (a) How many solutions are there to the equation x1 + x2 +x3 + x4 = 19 where zi, Z2, Z3, and4 are nonnegative integers? (b) What if we also require that each , must be at least 2? (c) What if we require that each must be at least 2, but r4 must also be at most 7? Hint: how maany solutions are there where 4 is greater than 7, and why is this relevant? 3. How many integer solutions are there to the equation 20 where each ri is at Hint: is there some way to "tweak" the equation so that we're using nonnegative variables? least-5?

Explanation / Answer

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Given that there are 5000 people to cast their votes and 4 number of candidates.

'=> Each student has 4 number of possibilities to cast their vote.

Total Number of ways in which votes can be casted are

= 4^5000

Solution

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