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... q letters p of which are alike . 1st . With the q unlike letters we can form C , r - combina- tions . 2nd . Taking one of the p letters ... COMBINATIONS WITH REPETITION 11 In the first place , Combinations when certain letters are alike.
... q letters $ p + p of which are alike . 1st . With the q unlike letters we can form C , r - com- binations . 2nd . Taking one of the p letters , and r - 1 of the q , we ... COMBINATIONS WITH REPETITION 11 In the 10 CH . XXIII P LETTERS ALIKE.
... q letters p of which are alike . 1st . With the q unlike letters we can form C , r - combina- tions . 2nd . Taking one of the p letters ... COMBINATIONS WITH REPETITION 11 In the first place , Combinations when certain letters are alike.
... q combinations from one of them , and p.q combinations from all of them . in ... repetition ) be made of them , including their rth powers and the products ... combinations of r letters , without repetitions , of ( n + r - 1 ) letters ...
... combinations of a1 .. a and q together without repetitions , and H , ( a , ... ap ) denote the combinations of a , ... ap , q and q together with repetitions , then making all the a's vanish , q and - ... p x — ap = $ ( — ) 1Cq ( α1 ...
... combinations . Ч Thus , for instance , if C ( a , ... a ) denote the combinations of a , ... ap , q and together without repetitions , and Hq ( a , ... ap ) denote the combinations of a , ... ap , q and q together with repetitions ...
... combinations of a1 ... ap , q and q together without repetitions , and H , ( a , ... a ) denote the combinations of a , ... a ,, q and q together with repetitions , then making all the a's vanish , and x - a , ... x - a = S , " ( — ) oC ...
... Q , Combination , & c . Let every box be marked with a letter , P , & c . , and in every case of the last let each counter take the letter of the box it is in . Either of the preceding problems then is the following : How many combinations ...
... combinations of numbers 1 to m taking 9-1 at a time and the number of combinations q - 1 at a time when each number is repeated ... repetition when two or more letters are repeated one or more times . Each combination determines the literal ...
... q + r + · ... things , when p things are alike , q things alike , r things alike , and so on ; of some or all of n different things . 13. The value of r that makes Cn the greatest 266 PERMUTATIONS , COMBINATIONS , PROBABILITIES . [ IX ,