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How do you write the permutation and combination formulas using latex. This is the best I can do:
[tex]n_P_r=\frac{n!}{(n-r)!}[/tex]
[tex]n_P_r=\frac{n!}{(n-r)!}[/tex]
Permutations are arrangements where the order matters, while combinations are selections where the order does not matter.
The permutation formula is written as nPr = $\frac{n!}{(n-r)!}$, where n is the total number of objects and r is the number of objects being selected.
The combination formula is written as nCr = $\frac{n!}{r!(n-r)!}$, where n is the total number of objects and r is the number of objects being selected.
Yes, the permutation and combination formulas can be used to solve real-life problems such as counting the number of possible outcomes in a game or the number of ways to arrange a group of people in a line.
Yes, there are several shortcuts and tricks such as using factorial notation, using the "n choose r" notation for combinations, and using the multiplication and addition principles for counting. It is important to understand the underlying concepts and formulas, but these shortcuts can make solving problems faster and easier.