How many ways can three of the letters of the word ALGORITHM be selected and written in a row? (1b) How many ways can three of the letters of the word ALGORITHM be selected and written in a row but where we do wish to account for the order of 3 letters? That is, the selection ALG is considerd the same as GLA and the also the same as LGA, and thus, these 3 orderings should only be counted once. (1c) How many ways can six letters of the word ALGORITHM be selected and written in a row if the first letter must be an A? (1d) How many ways can six letters of the word ALGORITHM be selected and written in a row if the first letter must be an A?, but where order is not important?
Suppose we are given the letters to the word ALGORITHM for which we’d like to study the number of permutations and combinations of various subsets of this set of letters.
(1a) How many ways can three of the letters of the word ALGORITHM be selected and written in a row?
(1b) How many ways can three of the letters of the word ALGORITHM be selected and written in a row but where we do wish to account for the order of 3 letters? That is, the selection ALG is considerd the same as GLA and the also the same as LGA, and thus, these 3 orderings should only be counted once.
(1c) How many ways can six letters of the word ALGORITHM be selected and written in a row if the first letter must be an A?
(1d) How many ways can six letters of the word ALGORITHM be selected and written in a row if the first letter must be an A?, but where order is not important?
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