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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.
Choose the correct answer/s. Choose E if none of the choices is correct.
![12. If a curve C moves along the same path of the vector field,
A. then the line integral is negative.
B. then the line integral is positive.
C. then the work done in the force fieldis negative.
D. then the work done in the force field is positive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4996dd58-e193-4da0-9b1b-a6a0aac8689c%2F8e23bbb5-3681-42dd-8fb2-c7456dacc745%2Fv3y6kx_processed.png&w=3840&q=75)
![11. In line integrals, if x(t) has a derivative equal to 0, with y'(t) and z'(t) not equal to 0,
A. then the line integral does not exist.
B. the resulting integrand will just become a pure function of y and z.
C. theresulting integrand will still be a function of x, y, and z.
D. x(t) must be a constant, other than 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4996dd58-e193-4da0-9b1b-a6a0aac8689c%2F8e23bbb5-3681-42dd-8fb2-c7456dacc745%2Fzx3c12x_processed.png&w=3840&q=75)
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