Elementary AlgebraRivingtons, 1870 - Algebra |
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... PERMUTATIONS 287 · CHAPTER XXXIV . COMBINATIONS 291 • • CHAPTER XXXV . THE BINOMIAL THEOREM . POSITIVE INTEGRAL INDEX THE BINOMIAL THEOREM . FRACTIONAL AND NEGATIVE INDICES CHAPTER XXXVI . CHAPTER XXXVII . SCALES OF NOTATION • CHAPTER ...
... PERMUTATIONS 287 · CHAPTER XXXIV . COMBINATIONS 291 • • CHAPTER XXXV . THE BINOMIAL THEOREM . POSITIVE INTEGRAL INDEX THE BINOMIAL THEOREM . FRACTIONAL AND NEGATIVE INDICES CHAPTER XXXVI . CHAPTER XXXVII . SCALES OF NOTATION • CHAPTER ...
Page 288
... permutations in which b stands first , thus : : ba , bc , bd , ...... Similarly there will be n- 1 permutations in which c stands first and so of the rest . In this way we get every possible permutation of the n things taken two at a ...
... permutations in which b stands first , thus : : ba , bc , bd , ...... Similarly there will be n- 1 permutations in which c stands first and so of the rest . In this way we get every possible permutation of the n things taken two at a ...
Page 289
... permutations of the n things taken r at a time will be n . ( n - 1 ) . ( n - 2 ) ...... ( n − r + 1 ) . If then the formula holds good when then things are taken r - 1 at a time it will hold good ... permutations . Then PERMUTATIONS . 289.
... permutations of the n things taken r at a time will be n . ( n - 1 ) . ( n - 2 ) ...... ( n − r + 1 ) . If then the formula holds good when then things are taken r - 1 at a time it will hold good ... permutations . Then PERMUTATIONS . 289.
Page 290
... permutation could now be interchanged , each interchange giving rise to a new permu- tation , and thus from each single permutation we could form 1.2 ...... p permutations in all , and the whole number of per- mutations would be ( 1. 2 ...
... permutation could now be interchanged , each interchange giving rise to a new permu- tation , and thus from each single permutation we could form 1.2 ...... p permutations in all , and the whole number of per- mutations would be ( 1. 2 ...
Page 291
... permutations can be formed out of the letters in Algebra taken all together ? 10. The number of things : number of permutations of the things taken 3 at a time : 1:20 . How many things are there ? = 11. The number of permutations of m ...
... permutations can be formed out of the letters in Algebra taken all together ? 10. The number of things : number of permutations of the things taken 3 at a time : 1:20 . How many things are there ? = 11. The number of permutations of m ...
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Common terms and phrases
2ab+b² a+b-c a²+2ab+b² a²+b² Algebra arithmetic means Arithmetical Progression Cambridge coefficient College List Crown 8vo denominator denote difference Divide Dividend division divisor Edition equal Find the number Find the value following expressions gallons Geometrical Progression given greater Greek Hence Highest Common Factor integer less logarithms miles an hour Multiply negative Nonary number of permutations number of terms obtain positive proceed proper fraction q factors quadratic equation quantity quotient radix ratio remainder represent the number result Rivington's School rules scale whose radix School and College second term Senary shew shillings sides Simplify solve the equations square root Subtracting surds take the square things taken third Thomas Kerchever Arnold tion unknown symbol whole number
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Page 253 - ... if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth ; or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth ; or, if the multiple of Book V.
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Page 328 - A number is divisible by 11 if the difference between the sum of the digits in the even places and the sum of the digits in the odd places is either 0 or a multiple of 11.
Page 292 - Recall the general formula for the number of combinations of n different things taken r at a time, C(n,r) n\ r!(nr)!
Page 328 - Suppose that a*=n, then x is called the logarithm of n to the base a : thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number. The logarithm of n to the base a is written log.