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Question Number 157980 by zainaltanjung last updated on 30/Oct/21
Calculate this problem below a). ((7!)/((5−1)!)) =...... b). ((5!×3!)/(4!)) =...... c). 6! 4! =... d). ((7!)/(3!))×((2!)/(5!)) =......
$$\mathrm{Calculate}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{below} \\ $$$$\left.\:\:\:\:\:\:\:\:\mathrm{a}\right).\:\:\frac{\mathrm{7}!}{\left(\mathrm{5}−\mathrm{1}\right)!}\:=…… \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\mathrm{b}\right).\:\:\frac{\mathrm{5}!×\mathrm{3}!}{\mathrm{4}!}\:=…… \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}\right).\:\:\mathrm{6}!\:\mathrm{4}!\:=…\:\:\:\:\:\:\:\: \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\mathrm{d}\right).\:\:\frac{\mathrm{7}!}{\mathrm{3}!}×\frac{\mathrm{2}!}{\mathrm{5}!}\:=…… \\ $$
Answered by puissant last updated on 30/Oct/21
a) ((7!)/((5−1)!))=((7×6×5×4!)/(4!))=7×6×5=210 b) ((5!×3!)/(4!))=((5×4!×3!)/(4!))=5×6=30 c) 6!×4!=6×5×4^2 ×3^2 ×2^2 ×1^2 =17280 d) ((7!)/(3!))×((2!)/(5!))=((7×6×5!×2!)/(6×5!))=7×2!=14
$$\left.{a}\right) \\ $$$$\frac{\mathrm{7}!}{\left(\mathrm{5}−\mathrm{1}\right)!}=\frac{\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}!}{\mathrm{4}!}=\mathrm{7}×\mathrm{6}×\mathrm{5}=\mathrm{210} \\ $$$$\left.{b}\right) \\ $$$$\frac{\mathrm{5}!×\mathrm{3}!}{\mathrm{4}!}=\frac{\mathrm{5}×\mathrm{4}!×\mathrm{3}!}{\mathrm{4}!}=\mathrm{5}×\mathrm{6}=\mathrm{30} \\ $$$$\left.{c}\right) \\ $$$$\mathrm{6}!×\mathrm{4}!=\mathrm{6}×\mathrm{5}×\mathrm{4}^{\mathrm{2}} ×\mathrm{3}^{\mathrm{2}} ×\mathrm{2}^{\mathrm{2}} ×\mathrm{1}^{\mathrm{2}} =\mathrm{17280} \\ $$$$\left.{d}\right) \\ $$$$\frac{\mathrm{7}!}{\mathrm{3}!}×\frac{\mathrm{2}!}{\mathrm{5}!}=\frac{\mathrm{7}×\mathrm{6}×\mathrm{5}!×\mathrm{2}!}{\mathrm{6}×\mathrm{5}!}=\mathrm{7}×\mathrm{2}!=\mathrm{14} \\ $$
Commented by zainaltanjung last updated on 30/Oct/21
okey... brother. true answered
$$\mathrm{okey}…\:\mathrm{brother}.\:\mathrm{true}\:\mathrm{answered} \\ $$
Answered by MathsFan last updated on 30/Oct/21
a) ((7×6×5×4×3×2×1)/(4×3×2×1))=210 b) ((5×4!×1×2×3)/(4!))=30 c) 6! • 4! 6!=6×5×4×3×2×1 =720 4!=4×3×2×1 = 24 24×720 = 17 280 d) ((7×6^2 ×5!)/(3×2!))×((2!)/(5!)) = 7×2=14
$$\left.{a}\right)\:\frac{\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\cancel{\mathrm{3}×\mathrm{2}×\mathrm{1}}}{\mathrm{4}×\cancel{\mathrm{3}×\mathrm{2}×\mathrm{1}}}=\mathrm{210} \\ $$$$ \\ $$$$\left.{b}\right)\:\frac{\mathrm{5}×\cancel{\mathrm{4}!}×\mathrm{1}×\mathrm{2}×\mathrm{3}}{\cancel{\mathrm{4}!}}=\mathrm{30} \\ $$$$ \\ $$$$\left.{c}\right)\:\mathrm{6}!\:\bullet\:\mathrm{4}!\: \\ $$$$\:\:\:\:\mathrm{6}!=\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}\:=\mathrm{720} \\ $$$$\:\:\:\:\mathrm{4}!=\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}\:=\:\mathrm{24} \\ $$$$\:\mathrm{24}×\mathrm{720}\:=\:\mathrm{17}\:\mathrm{280} \\ $$$$ \\ $$$$\left.{d}\right)\:\frac{\mathrm{7}×\cancel{\mathrm{6}}\:^{\mathrm{2}} ×\cancel{\mathrm{5}!}}{\cancel{\mathrm{3}}×\cancel{\mathrm{2}!}}×\frac{\cancel{\mathrm{2}!}}{\cancel{\mathrm{5}!}}\:=\:\mathrm{7}×\mathrm{2}=\mathrm{14} \\ $$
Commented by zainaltanjung last updated on 30/Oct/21
Okey....thanks a lot. your?answered is true
$$\mathrm{Okey}….\mathrm{thanks}\:\mathrm{a}\:\mathrm{lot}.\: \\ $$$$\mathrm{your}?\mathrm{answered}\:\:\mathrm{is}\:\mathrm{true} \\ $$

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