Callie,
Use the combination formula here, since order doesn't matter.
C(25,5) = 25!/[5!(25-5)!] = 53,130 ways!
I hope this helps, and have fun mathing!
LizZ
Callie L.
asked • 07/19/22You distribute 25 identical pieces of candy among five children. In how many ways can this be done?
More
1 Expert Answer
Still looking for help? Get the right answer, fast.
Ask a question for free
Get a free answer to a quick problem.
Most questions answered within 4 hours.
OR
Find an Online Tutor Now
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
Mitch C.
I disagree with this answer. C(25,5) is just the way to choose 5 pieces of candy from 25, and thus giving only one candy to each. What we want is to distribute the 25 candies. This is equivalent to solving a+b+c+d+e=25, where each letter corresponds to the number of candies received by a child. In other words, we are looking for 25 multisets made from {a,b,c,d,e}, for example [a,a,a,a,a,a,b,b,b,b,b,b,b,b,b,b,c,c,c,c,c,d,d,d,d]. Here, each letter tells us how many pieces of candy a child receives. According to the stars and bars model, there are C(25+5-1,25) = C(29,25) = 23,751 ways :)06/14/23