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If ¹²P_r = ¹¹P₆ + 6· ¹¹P₅, then the value of r is:
- 6
- 5
- 7
- None of these
Correct answer: 6
Solution
The equation represents a relationship between permutations, where the left side calculates the permutations of 12 items taken r at a time, and the right side combines permutations of 11 items taken 6 and 5 at a time, adjusted by a factor of 6. Solving this equation shows that r must equal 6 to satisfy the equality.
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