8 children, called Felix, Lana, Adam, Shaa, Fred, John, Eric and Aral are playing a game where they make new words out of their first name initials. a. How many distinct six-letter words that have two ’A’ and two ’F’ but only one ’L’ can they make out of their initials? b. How many distinct six-letter words that have two ’A’ and two ’F’ (and no restrictions on ’L’) can they make out of their initials? NOTE: (The initial of each person can only be used at most once, that is, ’F’, ’L’ and ’A’ at most twice and ’J’ and ’E’ at most once; a word is here defined as a sequence of letters, regardless of whether it makes sense in the English language.)
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
8 children, called Felix, Lana, Adam, Shaa, Fred, John, Eric and Aral are playing a game where they make new words out of their first name initials.
a. How many distinct six-letter words that have two ’A’ and two ’F’ but only one ’L’ can they make out of their initials?
b. How many distinct six-letter words that have two ’A’ and two ’F’ (and no restrictions on ’L’) can they make out of their initials?
NOTE: (The initial of each person can only be used at most once, that is, ’F’, ’L’ and ’A’ at most twice and ’J’ and ’E’ at most once; a word is here defined as a sequence of letters, regardless of whether it makes sense in the English language.)
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