Question 231962
think of the committee as two sub-committees, Physicians and Non-physicians


there is 1 way to have 6 Physicians (6C6) on the committee and 44C4 ways to fill the other 4 spots ___ (6C6 * 44C4) ways


there are 6C5 ways to have 5 Physicians and 44C5 ways to fill the remaining spots ___ (6C5 * 44C5) ways


for 4 Physicians ___ (6C4 * 44C6) ways


for 3 Physicians ___ (6C3 * 44C7) ways


the solution is the SUM of all 4