Elements

If the number of elements is decreased by two, the number of permutations decreases 30-fold. How many elements are there?

Final Answer:

n =  6

Step-by-step explanation:

P(n)=n! P(n) = 30 P(n−2) n! = 30 (n−2)! n(n−1)(n−2)! = 30 (n−2)! n(n−1)=30  n2−n−30=0  a=1;b=−1;c=−30 D=b2−4ac=12−4⋅1⋅(−30)=121 D>0  n1,2​=2a−b±D​​=21±121​​ n1,2​=21±11​ n1,2​=0.5±5.5 n1​=6 n2​=−5  n=n1​=6

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You need to know the following knowledge to solve this word math problem:

combinatoricsalgebrabasic operations and conceptsGrade of the word problem

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