53. A person has 12 friends out of which 7 are politicians and 5 are doctors. In how many ways he can invite
6 friends such that at least 3 politicians and atleast one doctor should be there in party.
a) 596
b) 582
c) 800
d) 805
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Answer:
d) 805
Step-by-step explanation:
Case 1- politicians- 3; doctors-3
Total number of ways= 7C3*5C3= 350
Case 2- politicians- 4; doctors-2
Total number of ways= 7C4*5C2= 350
Case 3- politicians- 5; doctors-1
Total number of ways= 7C5*5C1= 105
Number of ways he can invite 6 friends such that at least 3 politicians and atleast one doctor should be there in party= 350+350+105= 805
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