Binomial Probability question (1 Viewer)

[aonin]

From Independent Trial HSC 2006
Q4
Bob chooses six numbers from the numbers 1 to 4 inclusive. A machine then chooses six numbers at random from the numbers 1 to 40 inclusive. Find the probability that none of Bob's numbers match the numbers chosen by the machine, giving the answer to 2 decimal places

The answer was 34C6/40C6=0.35

Lol can someone help me understand the basis of the logic/answer, I don't get fully why there's a 40C6 and 34C6

 

[deterministic]

Number of ways for none of Bob's numbers to be chosen = 34C6 (from the 34 numbers which Bob didn't choose, choose 6 of them)
Total number of ways of choosing 6 numbers from 40 = 40C6

Hence Probability = Favourable/Total = 34C6/40C6

 

[aonin]

Thanks, got it now