SOLUTION: My teacher and I cannot figure this out. Please help us. A lodge has 50 members of whom six are physicians. In how many ways can you choose a committe of 10 that the committe c

Algebra ->  Permutations -> SOLUTION: My teacher and I cannot figure this out. Please help us. A lodge has 50 members of whom six are physicians. In how many ways can you choose a committe of 10 that the committe c      Log On


   

Question 231962: My teacher and I cannot figure this out. Please help us.
A lodge has 50 members of whom six are physicians. In how many ways can you choose a committe of 10 that the committe contains at least three physicians?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
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