Assume that the playbook contains 9 passing plays and 15 running plays. The coach randomly selects 8 plays from the playbook. What is the probability that the coach selects at least 2 passing plays and at least 3 running plays?

Answer = probability that he selects exactly 2,3,4 or 5 passing plays. prob that he selects exactly two passing plays = (8C2) * (9*8) * (15*14*13*12*11*10) / (26*28 * ... 19) where: 8C2 is the number of ways of choosing two slots out of 8 and prob that he selects first passing play = 9/26 prob that he select second passing play = 10/25 etc you can calculate the other three cases similarly and sum to obtain the answer.