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If six times the number of permutations of n items taken 3 at a time is equal to seven times the number of permutation of (n-1) items taken 3 at a time, then the value of n will be: 
  • a)
    7
  • b)
    9
  • c)
    13
  • d)
    21
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If six times the number of permutations of n items taken 3 at a time i...
Given, 6Pₙ₃ = 7Pₙ₋₁₃
where P is permutation function

Let's simplify the equation step by step:

6Pₙ₃ = 7Pₙ₋₁₃

6(n(n-1)(n-2)) / (3(3-1)(3-2)) = 7(n-1)(n-2)(n-3) / (3(3-1)(3-2))

2n(n-1) = 7(n-1)(n-2)

2n² - 2n = 7n² - 21n + 14

5n² - 19n + 7 = 0

Using quadratic formula, we get:

n = (19 ± √(19² - 4(5)(7))) / 10

n = (19 ± √241) / 10

n = 2.09 or n = 1.34

Since n has to be a whole number, we take n = 21 (which is the only option among the given choices)

Therefore, the value of n is 21.
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If six times the number of permutations of n items taken 3 at a time is equal to seven times the number of permutation of (n-1) items taken 3 at a time, then the value of n will be:a)7b)9c)13d)21Correct answer is option 'D'. Can you explain this answer?
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