j.shivank wrote:
Dear
Bunuel chetan2uWhat if we first select 1 individual from each set of couple and then out of those individuals, select 4 individuals.
(2C1 * 2C1 * 2C1 * 2C1 * 2C1 * 2C1) * 6C4
= 960
Then,
Total no. of ways to choose 4 people out of 12 is = 12C4
= 495
But turns out that this method is wrong as the probability comes out to be greater than 1
Can please help in pointing out why selecting 6 individuals from 6 couples first, is wrong?
There are repetitions in this..
One example..
Say 1-2, 3-4,5-6,7-8,9-10,11-12 are pair..
Select one out of each 1,3,5,7,9,11 choose ways of choosing 4: two ways would be 1,3,5,7 or 1,3,5,9
Now, choose one as 1,3,5,7,9,12 4: two ways would be 1,3,5,7 or 1,3,5,9
Not only these two, there will be many repetitions..
That is why you get probability more than 1..
But if you take 12 people first, remove the partner of the one you have chosen ..
So 10 left, close one , and again remove the partner..
Now you are left with 8...
And so on
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html
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