MHB Number of Ways to Select 3 Men & 3 Women from 5 Married Couples

  • Thread starter Thread starter Punch
  • Start date Start date
  • Tags Tags
    Permutation
AI Thread Summary
To determine the number of ways to select 3 men and 3 women from 5 married couples with exactly 2 married couples, first select 2 couples from the 5. Next, choose 1 man from the remaining 3 men, ensuring he is not married to any of the selected women. Additionally, select 1 woman from the 2 women not married to the chosen man. This structured approach ensures compliance with the requirement of including exactly 2 married couples in the selection.
Punch
Messages
44
Reaction score
0
Find the number of ways of selecting 3 men and 3 women from 5 married couples such that there are exactly 2 married couples.

I need the reasoning
 
Mathematics news on Phys.org
First you select two couples out of five. Then you select one man out of the remaining three and one of the two women who are not his spouse.
 
Punch said:
Find the number of ways of selecting 3 men and 3 women from 5 married couples such that there are exactly 2 married couples.
I need the reasoning
Choose three wives. From their husbands choose two. Then choose one of the other men not married to any of the three chosen wives.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

MHB -ratio to ratio club membership
Replies
2
Views
1K
MHB Probability of 3 people ending up on same team?
Replies
5
Views
4K
MHB Solve Seating Arrangement of 4 Men and 4 Women No Pair Next
Replies
1
Views
2K
MHB Is $p\equiv 3\pmod{4}$ a condition for $\pi$ to be an even permutation?
Replies
1
Views
1K
MHB Calculate the probability and the number of ways
Replies
12
Views
4K
Find the ratio of men to women
Replies
1
Views
1K
MHB In how many ways can we create such a committee?
Replies
2
Views
1K
B Optimizing permutations of hero traits in a computer game
Replies
2
Views
1K
How many ways are there for four men and five women ...
Replies
7
Views
10K
MHB Is one form of the answer more right than the other
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top