The urn contains 10 white, 15 black, 20 blue, 25 red balls. What is the probability that out

The urn contains 10 white, 15 black, 20 blue, 25 red balls. What is the probability that out of seven balls drawn: 2 white, 3 black and 2 red balls

1. Let:

n1 = 10 white balls;
n2 = 15 black;
n3 = 20 blue;
n4 = 25 red;
n = 70 total balls;
k = 7 – out of 7 taken out balls;
k1 = 2 white;
k2 = 3 black;
k3 = 0 blue;
k4 = 2 red.
2. Let’s use the formula:

P = С (n1, k1) * С (n2, k2) * С (n3, k3) * С (n4, k4) / C (n, k), where
C (n, k) = n! / (K! * (N – k)!) Are binomial coefficients.
P = C (10, 2) * C (15, 3) * C (20, 0) * C (25, 2) / C (70, 7);
P = 10! / (2! * 8!) * 15! / (3! * 12!) * 20! / (0! * 20!) * 25! / (2! * 23!): 70! / ( 7! * 63!);
P = 45 * 455 * 1 * 300: 1 198 774 720 ≈ 0.0051.
Answer: 0.0051.