What is the probability that a husband and wife do not belong to that committee?

A committee of 5 people is randomly selected from 6 married couples (12 people). What is the probability that a husband and wife do not belong to that committee?What is the probability that a husband and wife do not belong to that committee?
Total combinations = 12C5





Favourable cases-





Ways to select first member = 12


second member no. of ways = 10 (excluding the spouse of first one)


third = 8 (excluding spouses of first 2)


fourth = 6 (excluding spouses of first 3)


fifth = 4 (excluding spouses of all 4)





Multiply and get the possibile conditions = 12*10*8*6*4





Probability =


12C5 / 12*10*8*6*4





(8*9*10*11*12/2*3*4*5) / 12*10*8*6*4


= 6*11*12 / 12*10*8*6*4


= 11 / 10*4*8


= 11 / 320





Hope this helps !What is the probability that a husband and wife do not belong to that committee?
1 - P(Both Belong To Committee) =





1 - [(10 Ncr 3) / (12 Ncr 5)] =





1 - [120 / 792] =





1 - .151515... =





.848484... =





28/33












You must choose one or none from each couple, so it's 2* 6C5


2( 6C5 )=2(1/6)=1/3