If there are N in total in the bag, including B blues. N is greater than or equal to 20 and N-B are not blue. The values of N and B haven't been given. The probability of selecting one blue is B/N and of selecting a different colour is (N-B)/N or 1-(B/N). Having selected a blue already, there are now N-1 M&Ms left in the bag, including B-1 blues. The probability of selecting a second blue is (B-1)/(N-1); the probabilities of a third, fourth and fifth blue are respectively (B-2)/(N-2), (B-3)/(N-3), (B-4)/(N-4). The combined probability is B(B-1)...(B-4)/(N(N-1)...(N-4)). We now have all the blues we need, so the remaining 15 sweets must be non-blue. So we continue with the sixth selection: (N-B)/(N-5); and the 7th: (N-B-1)/(N-6), and so on up to the 20th: (N-B-9)/(N-14). Combine the product of these probabilities with the earlier ones and we get: B(B-1)...(B-4)(N-B)(N-B-1)...(N-B-9)/(N(N-1)...(N-14)). Call this P.
But we're not finished, because we have only included one permutation, that where 5 blues come first and 15 non-blues follow. We're only interested in the combination of blues and non-blues, not their order. So we need to multiply our combined probability by the number of different ways we can arrange 5 blues and 15 non-blues. This is given by the expression: 20*19*18*17*16/(1*2*3*4*5)=15504. Mathematically it's represented by the nCr function, which produces the number of ways of arranging r objects out of n objects. nCr=nC(n-r) so 20C15 is the same number as 20C5. We have only two types of object, blue and non-blue sweets, so the combined probability we got earlier is too low by a factor of 15504, so the true answer is 15504P.