In the questions below suppose that a “word” is any string of seven letters of the alphabet, with repeated letters allowed. a) How many words begin with R and end with T? b) How many words begin with A or B? c) How many words begin with A or end with B?
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.
Q‒1) In the questions below suppose that a “word” is any string of seven letters of the alphabet, with repeated letters allowed.
a) How many words begin with R and end with T?
b) How many words begin with A or B?
c) How many words begin with A or end with B?
d) How many words begin with A or B and end with A or B?
e) How many words begin with A or B or end with A or B?
f) How many words begin with a vowel and end with a vowel?
g) How many words begin with a vowel or end with a vowel?
h) How many words begin with AAB in some order?
i) How many words have no vowels?
j) How many words have exactly one vowel?
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