azamaka wrote:
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
A) 564
B) 645
C) 735
D) 756
E) 566
Hi
A quick observation..
Ans will have selection of atleast 3 from 7 men, so the answer has to be a multiple of 7..
So ONLY C and D are left..
A high probability to get your answer correct even if you did not know what to do..
Now TWO ways..
1) Now select 3 from 7 and select next 2 from remaining 6 females Or both from males or one each..
And the solution as mentioned above will be
7C5+7C4*6C1+7C3*6C2=21+35*6+35*15=756..
2) Another way total ways - ways where 3 males are not there..
All females 6C5=6..
All but one 6C4*7C1=15*7=105
All but 2..6C3*7C2= 20*21=420
So ways where 3 males are not there 6+105+420=531..
Total 13C5= 13*12*11*10*9/(2*3*4*5)= 13*11*9=1287..
So remaining ways = 1287-531=756..
D
A quick observation..
Ans will have selection of atleast 3 from 7 men, so the answer has to be a multiple of 7.
- Sachin
-If you like my explanation then please click "Kudos"