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Question Number 157980 by zainaltanjung last updated on 30/Oct/21

$$\mathrm{Calculate}\mathrm{this}\mathrm{problem}\mathrm{below}$$$$\mathrm{a}).\frac{7!}{(5-1)!}=......$$$$\mathrm{b}).\frac{5!\times 3!}{4!}=......$$$$\mathrm{c}).6!4!=...$$$$\mathrm{d}).\frac{7!}{3!}\times \frac{2!}{5!}=......$$

Answered by puissant last updated on 30/Oct/21

$$a)$$$$\frac{7!}{(5-1)!}=\frac{7\times 6\times 5\times 4!}{4!}=7\times 6\times 5=210$$$$b)$$$$\frac{5!\times 3!}{4!}=\frac{5\times 4!\times 3!}{4!}=5\times 6=30$$$$c)$$$$6!\times 4!=6\times 5\times 4^2\times 3^2\times 2^2\times 1^2=17280$$$$d)$$$$\frac{7!}{3!}\times \frac{2!}{5!}=\frac{7\times 6\times 5!\times 2!}{6\times 5!}=7\times 2!=14$$

Commented by zainaltanjung last updated on 30/Oct/21

$$\mathrm{okey}...\mathrm{brother}.\mathrm{true}\mathrm{answered}$$

Answered by MathsFan last updated on 30/Oct/21

$$a)\frac{7\times 6\times 5\times 4\times \cancel{3\times 2\times 1}}{4\times \cancel{3\times 2\times 1}}=210$$$$$$$$b)\frac{5\times \cancel{4!}\times 1\times 2\times 3}{\cancel{4!}}=30$$$$$$$$c)6!\bullet 4!$$$$6!=6\times 5\times 4\times 3\times 2\times 1=720$$$$4!=4\times 3\times 2\times 1=24$$$$24\times 720=17280$$$$$$$$d)\frac{7\times \cancel{6}{}^2\times \cancel{5!}}{\cancel{3}\times \cancel{2!}}\times \frac{\cancel{2!}}{\cancel{5!}}=7\times 2=14$$

Commented by zainaltanjung last updated on 30/Oct/21

$$\mathrm{Okey}....\mathrm{thanks}\mathrm{a}\mathrm{lot}.$$$$\mathrm{your}?\mathrm{answered}\mathrm{is}\mathrm{true}$$

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