2004
Mathematics
67ca00ce0c643c71d77dee1f
A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the members of the committee be chosen so as to include one member of the house of assembly
A.
378 ways
B.
462 ways
C.
840 ways
D.
924 ways
Correct Answer: 924 ways
Explanation
3C1 ×9 C5=3!/((3-1)!1!)×9!/((9-5)!5!) "\= " 3!/2!1!×9!/4!5! "\=" (3×2!)/(2!×1)×(9×8×7×6×5!)/(4×3×2×1×5!) "\=" 3×9×2×7"\=" 378ways
3C1 ×9 C5=3!/((3-1)!1!)×9!/((9-5)!5!) "\= " 3!/2!1!×9!/4!5! "\=" (3×2!)/(2!×1)×(9×8×7×6×5!)/(4×3×2×1×5!) "\=" 3×9×2×7"\=" 378waysTHIS WEEK's
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