SOLUTION: There are 5 boys and 6 girls on a grad committee In how many ways can a sub-committee of 4 people can be selected if there must be at least 1 girl on the sub-committee?

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Question 23232: There are 5 boys and 6 girls on a grad committee
In how many ways can a sub-committee of 4 people can be selected if there must be at least 1 girl on the sub-committee?

Answer by venugopalramana(3286) About Me  (Show Source):
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There are 5 boys and 6 girls on a grad committee
In how many ways can a sub-committee of 4 people can be selected if there must be at least 1 girl on the sub-committee?
THERE SHOULD BE ATLEAST 1 GIRL IN THE COMMITTEE.SO THERE COULD BE 1 OR 2 OR 3 OR 4 IN THE 4 MEMBER COMMITTEE.INSTEAD OF WORKING SO MANY ALTERNATIVES ,IT IS EASIER TO WORK OUT A COMMITTEE WITH NO GIRLS AND SUBTRACT IT FROM TOTAL POSSIBILITIES OF 4 MEMBER COMMITTES
THERE ARE 5 BOYS+6 GIRLS=11 PERSONS
TOTAL NUMBER OF 4 MEMBER COMMITTEES THAT COULD BE FORMED=11C4=11!/(4!7!)
=11*10*9*8/(4*3*2*1)=330
NUMBER OF COMMITTES WITH NO GIRLS......THAT MEANS WE CAN SELECT 4 PERSONS FROM 5 BOYS DISABLED_event_ONLY= IN 5C4 WAYS=5!/(4!1!)=5 WAYS
HENCE NUMBER OF POSSIBLE COMMITTES WITH AT LEAST ONE GIRL = 330-5=325