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Probability Level 2

There are 3 types of menu, namely noodle, chicken, fish, avaible in restaurant. A boy wishes to place an order of 8 menu (so he want to take 8 portion food). Assuming that there is no limit in the supply of each type, how many such orders can the boy place?

source : Chen Chuan Chong's book.

Image credit: Wikipedia NewtonYAU


The answer is 45.

Vederis Leunardus by Vederis Leunardus , 24, Indonesia

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1 solution

we make it simple - a + b + c = 8; - 0000000011 // we asume that 11 is the operand (+) so the answer is C(10,2)

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Mayank Holmes - 6 years, 11 months ago

each order can be placed in 3 different ways ........ so total number of ways of placing 8 orders is 3^(8)

Mayank Holmes - 6 years, 11 months ago

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ok, i will try simplify, a + b = 2; if you follow my way above you will get : C(3,1) / / so lets try do it manually : 0 + 2 = 2 1 + 1 = 2 2 + 0 = 2 if we assume your way is true : this is could be 2^2 = 4; thanks for comment :) i hope you can understand it :) sorry for my bad english

Vederis Leunardus - 6 years, 11 months ago

You need to distinguish between applying the "rule of product" and applying "stars and bars". In this case, we have 3 distinct boxes (the menu items), and 8 indistinguishable balls (the orders), hence we apply "stars and bars" instead.

Calvin Lin Staff - 6 years, 11 months ago

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