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

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If 10Pr = 5040, then r = ?
Correct answer is '4'. Can you explain this answer?

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We know that
nPr = 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 = 4
Hence, the correct answer is 4.

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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.