Choose three wives. From their husbands choose two. Then choose one of the other men not married to any of the three chosen wives.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
The total number of ways to select 3 men and 3 women from 5 married couples is 10. This can be calculated using the combination formula: nCr = n!/(r!(n-r)!), where n is the total number of options and r is the number of options to be selected.
No, the same person cannot be selected for both the men and women groups. This is because the question specifies 3 men and 3 women, not 6 individuals. Therefore, each person can only be selected once.
If we have 6 married couples instead of 5, the number of ways to select 3 men and 3 women would increase to 20. This is because there would be more options to choose from, increasing the total number of possible combinations.
No, the order of selection is not important in this scenario. As long as we end up with 3 men and 3 women, the specific order in which they are selected does not matter. Therefore, we use the combination formula rather than the permutation formula.
The number of ways to select 2 men and 4 women from 5 married couples is 10. This is because we are still selecting a total of 6 individuals, but now the ratio is 2:4 instead of 3:3. Therefore, the same combination formula applies.