Find the value of 6P2×5P3
Solution
Correct Answer: Option E
We know that:
Formula:
\({}_{}^n{P_r} = \frac{{!n}}{{!\left( {n - r} \right)}}\)
∴6P2 × 5P3 = \(\frac{{!6}}{{!\left( {6 - 2} \right)}} \times \frac{{!5}}{{!\left( {5 - 3} \right)}}\)
⇒6P2 × 5P3 \(= \frac{{!6}}{{!4}} \times \frac{{!5}}{{!2}}\)
⇒6P2 × 5P3 = \(\frac{{6 \times 5 \times 4 \times 3 \times 2 \times 1}}{{4 \times 3 \times 2 \times 1}} \times \frac{{5 \times 4 \times 3 \times 2 \times 1}}{2}\)
⇒6P2 × 5P3 = 30 × 60
⇒6P2 × 5P3 = 1800
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