St. Ives The following is a well-known children’s rhyme:As I was going to St. Ives,I met a man with seven wives;Every wife had seven sacks;Every sack had seven cats;Every cat had seven kits;Kits, cats, sacks, and wives,How many were going to St. Ives?Assuming that the entire group is actually going to St. Ives,show that the answer to the question in the rhyme is a partialsum of a geometric sequence, and find the sum.
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.
St. Ives The following is a well-known children’s rhyme:
As I was going to St. Ives,
I met a man with seven wives;
Every wife had seven sacks;
Every sack had seven cats;
Every cat had seven kits;
Kits, cats, sacks, and wives,
How many were going to St. Ives?
Assuming that the entire group is actually going to St. Ives,
show that the answer to the question in the rhyme is a partial
sum of a geometric sequence, and find the sum.
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