In a bag, there are 10 discs, numbered 1 to 10 (no duplicates). If we randomly choose 4 of the discs, what is the probability that the range of the numbers chosen is 7?
Choose the correct choice from the following
A) 1 / 14	B) 1 / 7	C) 3 / 14	D) 9 / 28	E) 4 / 7
Probability (A) = No of suitable outcomes where A happens/Total no of outcomes   We use combinations to get "No of suitable outcomes where A happens" and "Total no of outcomes" and then calculate the required probability. So for the time being, just forget that you have to find some probability.   Focus on two things: "No of suitable outcomes where A happens" and "Total no of outcomes"   It is easy to find total number of outcomes. 10C4. e.g. (2, 3, 4, 6), (4, 1, 9, 5) etc etc etc   In how many combinations is range 7? (This is the "No of suitable outcomes where A happens")   (3, 10, a, b), (2, 9, c, d) and (1, 8, e, f)   a and b are numbers between 3 and 10 (so that range doesn't exceed 7)   c and d are numbers between 2 and 9   e and f are numbers between 1 and 8   In how many ways can you choose a and b? 6C2 (Any 2 out of 6 numbers between 3 and 10). So how many 4 number combinations are there which look like this: (3, 10, 4, 6), (3, 10, 7, 5) etc?   I hope you agree it is 6C2.   Similarly, you get 6C2 combinations of the type (2, 9, c, d) and 6C2 of the type (1, 8, e, f).   No of suitable combinations = 63 / 142 + 63 / 142 + 63 / 142   Now, the required probability = No of suitable combinations where A happens/Total no of outcomes   = (3*63 / 142)/103 / 144 =3/14   3 / 14orrect answer is 3 / 14
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In a bag, there are 10 discs, numbered 1 to 10 (no duplicates). If we randomly choose 4 of the discs, what is the probability that the range of the numbers chosen is 7?