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Math Help - combinations

  1. #1
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    combinations

    Q. The integers from 1 to 9 inclusive are written on 9 cards, which are shuffled. 3 cards are then drawn at random. Find the probability that the numbers on these cards are consecutive?

    The mark scheme tells me this:
    1-No of ways of drawing 3 cards= (9x8x7)/6=84
    2-No of consecutive triads = 7, so P (consecutive)= 1/12


    I understand most of this, but am not sure why you divide by 6 in step one.
    Help would be greatly appreciated!

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  2. #2
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    Quote Originally Posted by orangesmarties View Post
    Q. The integers from 1 to 9 inclusive are written on 9 cards, which are shuffled. 3 cards are then drawn at random. Find the probability that the numbers on these cards are consecutive?

    The mark scheme tells me this:
    1-No of ways of drawing 3 cards= (9x8x7)/6=84
    2-No of consecutive triads = 7, so P (consecutive)= 1/12

    I understand most of this, but am not sure why you divide by 6 in step one.
    Help would be greatly appreciated!

    6 = 3!

    You're dividing by the number of arrangements of the three cards.
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