Solve this problem that involves combinations

In summary, the conversation is about finding the solution to a tricky question involving combinations and committees. One person is seeking an alternative approach and presents a solution of 110, while the other suggests an alternative method of counting committees and subtracting the ones with both cousins.
  • #1
chwala
Gold Member
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Homework Statement
see attached
Relevant Equations
combinations
1653300388407.png


My interest is on part b only.

I am seeking alternative approach to the problem. This was a tricky question i guess. Find my approach below;

##5C3×4C2 ##{senior cousin included and junior not included}+ ##5C4×4C1##{ senior cousin not included, Junior cousin included}+##5C4×4C2##{both NOT included}= ##60+20+30=110##

Wah...this really boggled my mind a little bit:biggrin:...i only have the text solution, which is 110.

Kindly check my working then any other better approach would be welcome. Cheers guys!
 
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  • #2
That looks fine. An alternative is to count the total number of committees and then subtract the number of committees that have both cousins.
 
Last edited:
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Likes Prof B and chwala

FAQ: Solve this problem that involves combinations

What are combinations?

Combinations are a mathematical concept that refers to the different ways in which a set of items can be selected and arranged without repetition.

How do I solve a problem involving combinations?

To solve a problem involving combinations, you need to first identify the number of items in the set and the number of items to be selected. Then, you can use the formula nCr = n! / r!(n-r)! where n is the total number of items and r is the number of items to be selected.

Can combinations be used in real-life situations?

Yes, combinations can be used in real-life situations such as creating passwords, lottery numbers, and selecting items from a menu or wardrobe.

What is the difference between combinations and permutations?

The main difference between combinations and permutations is that combinations do not consider the order of the selected items, while permutations do. In other words, combinations are used when the order does not matter, and permutations are used when the order does matter.

Are there any shortcuts for solving combination problems?

Yes, there are several shortcuts that can be used to solve combination problems, such as using the combination formula, using the combination calculator, or using the Pascal's triangle method. It is important to understand the concept behind combinations before using shortcuts to solve problems.

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