one:
First, I made it 5*6 = 30 instead of 4 x 6 because position 1 can be filled by any one person of the 5 married couples and next position has to be filled in one ways then the last position can be filled in 6 ways which makes it 30 instead of 24.
huh?
per the problem statement, there are four, not five, married couples.
go back and read the problem statement again.
two:
Secondly, I am not sure about this because you can choose A1 A2 * 6 or A2 A1 * 6 which makes 5 * 2 * 6.
no, you don't multiply this by two.
analogy #1:
if you have 3 shirts and 4 pairs of pants, then you have 3 x 4 = 12 outfits.
hopefully you consider that "obvious"; the multiplication principle at work here is probably the most basic principle in all of combinatorics.
the point, though, is that your approach above would give 3 x 4 x 2 = 24 outfits, an incorrect answer.
analogy #2:
there are 26 letters in the alphabet.
this question is sort of like saying: 'if i count all the letters in the alphabet forwards, and then i count them all backwards, i get a total of 52. so why aren't there 52 letters?'
answer:
once you've figured out one legitimate way to count something, you just count it that way. if you count the same things twice in two different ways, then you'll calculate twice the number you're supposed to get.
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now, if the ORDER in which you pick the couple and the lone individual mattered - i.e., if couple/individual differs in some way from individual/couple - then your approach would be correct.
Ron has been teaching various standardized tests for 20 years.
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