A student club consists of 14 girls and 16 guys. A committee of 8 is to...
A student club consists of 14 girls and 16 guys. A committee of 8 is to be selected. In how many ways can this be done if: A.) the committee must have at least 6 girls on it. B.) three officers (president, vice president, secretary/treasurer) are selected from ALL the members. Please show work.
Homework Answers
Ans:
A)
Case 1)When 6 girls,2 guys
Number of ways =14C6*16C2=360360
Case 2)When 7 girls,1 guy
Number of ways =14C7*16C1=54912
Case 2)When 8 girls
Number of ways =14C8=3003
Total number of ways=360360+54912+3003=418275
B)In this case order matters,so we use permutation.
Number of ways=30P3=24360
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