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Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

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November 18th, 2016, 03:07 PM   #1
Joined: Aug 2016
From: Santos-SP / BRASIL

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I need help!

(a) Using the concept of permutation with repetition, draw up and execute a plan of resolution that leads to determining the number of whole and not negative solutions of the equation:

x 1 + x 2 + x 3 + ... + xn = p.

(b) Solve the following problem:

How differently can we buy 3 full juice boxes in a supermarket that sells flavors: pineapple, lemon, orange, grape, apple, mango and peach?

Tip: Design an equation of this type in item (a), causing the problem appears if set in a particular case of this equation.

Last edited by skipjack; December 8th, 2016 at 02:12 PM.
Samuel Leite is offline  
December 8th, 2016, 10:53 AM   #2
Joined: Dec 2016
From: Geneva

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For question a, you can imagine p elements being shared between n groups. Say you line up your p elements, and place the n-1 limits between each groups. Counting the p elements and the limits, there are in all p+n-1 'places'. You need to choose n-1 to position your 'limits' or p of them to position your elements. There are p+n-1Cn-1 = p+n-1Cp solutions to your problem.

Question b is the same story. There are 3 juice boxes to be share through 7 fruit types. There are 9C6 = 9C3 = 84 possibilities.

I hope I was helpful.

Last edited by skipjack; December 8th, 2016 at 02:03 PM.
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