CAT Question > If 10Pr = 5040, then r = ?Correct answer is ...

If ^{10}P_{r }= 5040, then r = ?

Correct answer is '4'. Can you explain this answer?

We know that^{n}P_{r }= n!/(n−r)! = n × (n − 1)×….×(n−r+1)^{10}P_{r }= 5040

Given that:

⇒ 10Pr = 10 × 504

⇒ 10Pr = 10 × 9 × 56

⇒ 10Pr = 10 × 9 × 8 × 7

⇒ 10Pr = 10 × (10 − 1) × (10 − 2) × (10 − 4 + 1)

On comparing the above expression with ^{n}P_{r }= n × (n − 1)×……×(n − r + 1), we get:

r = 4

Hence, the correct answer is 4.

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### If 10Pr = 5040, then r =

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If 10Pr = 5040, then r = ?Correct answer is '4'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If 10Pr = 5040, then r = ?Correct answer is '4'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 10Pr = 5040, then r = ?Correct answer is '4'. Can you explain this answer?.

If 10Pr = 5040, then r = ?Correct answer is '4'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If 10Pr = 5040, then r = ?Correct answer is '4'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 10Pr = 5040, then r = ?Correct answer is '4'. Can you explain this answer?.

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We know thatnPr = n!/(n−r)! = n × (n − 1)×….×(n−r+1)Given that:10Pr = 5040⇒ 10Pr = 10 × 504⇒ 10Pr = 10 × 9 × 56⇒ 10Pr = 10 × 9 × 8 × 7⇒ 10Pr = 10 × (10 − 1) × (10 − 2) × (10 − 4 + 1)On comparing the above expression with nPr = n × (n − 1)×……×(n − r + 1), we get:r = 4Hence, the correct answer is 4.