## Mathematics: Compiled from the Best Authors, and Intended to be the Text-book of the Course of Private Lectures on These Sciences in the University at Cambridge, Volume 1W. Hilliard, 1808 - Mathematics |

### From inside the book

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Page 204

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**number**of things , taken a given**number**at a time ; in which there are several given things of one sort , several of another , & c . RULE . * 1. Find all the different forms of**combination**of all the given things , taken as many at a ... Page 205

... 10 , aaaabbccde ? Ans . 22260 . 3. How many different numbers can be made out of 1 unit , 2 twos , 3 threes , 4 fours , and 5 fives , taken 5 at a time ? Ans . 2111 . PROBLEM V. To find the

... 10 , aaaabbccde ? Ans . 22260 . 3. How many different numbers can be made out of 1 unit , 2 twos , 3 threes , 4 fours , and 5 fives , taken 5 at a time ? Ans . 2111 . PROBLEM V. To find the

**number of combinations**of any ARITHMETIC . 205. Page 206

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**number of combinations**of any given number of things , all different from one another , taken any given num- ber at a time . RULE . * 1. Take the series 1 , 2 , 3 , 4 , & c . up to the number to be taken at a time , and find the product ... Page 207

... number , out of which the election is to be made , and find the product of all the terms . 3. Divide the last product by the former , and the quo- tient will be the number sought . EXAMPLES . 1.

... number , out of which the election is to be made , and find the product of all the terms . 3. Divide the last product by the former , and the quo- tient will be the number sought . EXAMPLES . 1.

**How many combinations**can be made of 6 ... Page 208

... number from 10 ) = 15120O 720 ) 151200 ( 2:10 the answer . 1440 720 720 2.

... number from 10 ) = 15120O 720 ) 151200 ( 2:10 the answer . 1440 720 720 2.

**How many combinations**can be made of 2 ...**number of combinations**of any given number of thing? , by taking any given number at a time ; in which there are ...### Contents

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### Common terms and phrases

2qrs amount of 11 angle annuity annum answer required arithmetical called carats cent centre circle circumference coefficient common denominator completing the square compound interest cube root debt decimal denoted diameter discount Divide dividend division divisor equal equation EXAMPLES exponent figures Find the present fourth gallon geometrical progression geometrical series give given number greater greatest common measure improper fraction least common multiple less number logarithm manner Multiply natural number negative NOTE nth root number of combinations number of terms number of things payment perpendicular pound present worth PROBLEM proportion quotient radius ratio Reduce remainder repetend required to find rule of three sides simple interest sought square root subtract Suppose supposition surd taken tare triangle unknown quantity vulgar fraction Whence whole number yards