6 married couples are standing in a room. If 4
people are chosen at random, then the chance
that exactly one married couple is among the 4 is
(1)16/33 (2)8/33 (3)17/33 (4)24/33
Answers
Answered by
15
Answer:
16/33
Step-by-step explanation:
Consider married couple as M1F1, M2F2, M3F3, M4F4, M5F5, M6F6.
Cases where only married couple M1F1 is amongst selected :-
2 people are already selected M1F1, Remaining we have 2 position and 10 people. So number of combination possible is ¹⁰C₂ - 45. Out of those 45 we need to remove 5 combination of M2F2, M3F3, M4F4, M5F5, M6F6. So left combinations as 40.
So total combinations of exactly one married couple is among the 4 = 6 x 40 = 240
Total number of ways to select 4 people out of 12 is ¹²C₄ = 495
So, the chance
that exactly one married couple is among the 4 is = 240/495 = 16/33
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