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.
