Question 658817: the number of ways in which 12 mangoes can be equally divided among 3 student
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Hi, there--
You asking for a combination---the number of ways that n objects (mangoes) can be sub-divided into groups of r objects (students). We don't care what order the objects are in. Getting mango 1, mango 2, and mango 3 would be the same as getting mango 3, mango 1, and mango 2.
You sometimes hear this called "n choose r" or, in your problem, "12 choose 3." It can be written as 12C3. The formula is
nCr = n! / ((n-r)! * r!)
12C3 = 12! / ((12-3)! * 3!)
12C3 = 12! / (9! * 3!)
When you expand the factorials out, you will find that many factors cancel out.
12C3 = (12*11*10*9!) / (9! * 3*2*1)
12C3 = (12*11*10) / (3*2)
12C3 = 2*11*10
12C3 = 220
There 220 unique ways to divide 12 mangoes among 3 students.
Best,
Ms.Figgy
math.in.the.vortex@gmail.com
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