Solve this problem that involves combinations

  • Thread starter Thread starter chwala
  • Start date Start date
  • Tags Tags
    Combinations
AI Thread Summary
The discussion focuses on solving a combination problem, specifically part b, where the user presents their approach to calculating the total number of valid combinations involving senior and junior cousins. They detail their calculations, arriving at a total of 110 combinations. The user expresses some confusion and invites others to review their method and suggest alternative approaches. Another suggested method involves calculating the total number of committees and subtracting those that include both cousins. The conversation emphasizes the complexity of the problem and the search for clearer solutions.
chwala
Gold Member
Messages
2,827
Reaction score
415
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!
 
Physics news on Phys.org
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:
Reply
  • Like
Likes Prof B and chwala

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Solve the given problem involving probability without replacement
Replies
10
Views
3K
Solve the given problem that involves Trigonometry
Replies
7
Views
1K
Solve the given trigonometry problem
Replies
10
Views
2K
Solve for x and y in the given algebra problem involving fractions
Replies
25
Views
3K
Solving South America Combinations Problem: 210 Possibilities
Replies
9
Views
2K
Solve the given problem that involves Probability
Replies
2
Views
968
Prove the trigonometry identity and hence solve given problem
Replies
5
Views
2K
Solve the given problem that involves Test of Hypothesis
Replies
7
Views
2K
Solving equations of the form ##a\sin\theta+b\cos\theta = c##
Replies
2
Views
2K
I Solve Coin Sum Problem: Find Combinations for 200p
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top