Thread: 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!

Originally Posted by orangesmarties

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.