Five distinct integers are to be chosen from the set {1, 2, 3, 4, 5, 6, 7, 8} and placed in some order in the top row of boxes in the diagram. Each box that is not in the top row then contains the product of the integers in the two boxes connected to it in the row directly above. Determine the number of ways in which the integers can be chosen and placed in the top row so that the integer in the bottom box is 9 953 280 000.
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.
Five distinct integers are to be chosen from
the set {1, 2, 3, 4, 5, 6, 7, 8} and placed in some
order in the top row of boxes in the diagram.
Each box that is not in the top row then
contains the product of the integers in the
two boxes connected to it in the row directly
above. Determine the number of ways in
which the integers can be chosen and placed
in the top row so that the integer in the
bottom box is 9 953 280 000.
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