Question

from a group of 7 men and 6 women a committee of 5 persons with more males than the females is to be formed .in how many ways can be done ?

Answer 1

Answer:

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..

Answer 2

Answer:

2 ways.

1. 3 men and 2 women

2. 4 men and 1 women.

Hope this helps.

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