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compute p(n,r)for (i)n=8,r=2 (ii)n=10,r=...

compute p(n,r)for (i)n=8,r=2 (ii)n=10,r=3

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To compute \( P(n, r) \), we use the formula: \[ P(n, r) = \frac{n!}{(n - r)!} \] where \( n! \) denotes the factorial of \( n \). ### (i) For \( n = 8 \) and \( r = 2 \): 1. **Substitute the values into the formula**: \[ P(8, 2) = \frac{8!}{(8 - 2)!} = \frac{8!}{6!} \] 2. **Expand \( 8! \)**: \[ 8! = 8 \times 7 \times 6! \] 3. **Substitute back into the equation**: \[ P(8, 2) = \frac{8 \times 7 \times 6!}{6!} \] 4. **Cancel out \( 6! \)**: \[ P(8, 2) = 8 \times 7 = 56 \] ### (ii) For \( n = 10 \) and \( r = 3 \): 1. **Substitute the values into the formula**: \[ P(10, 3) = \frac{10!}{(10 - 3)!} = \frac{10!}{7!} \] 2. **Expand \( 10! \)**: \[ 10! = 10 \times 9 \times 8 \times 7! \] 3. **Substitute back into the equation**: \[ P(10, 3) = \frac{10 \times 9 \times 8 \times 7!}{7!} \] 4. **Cancel out \( 7! \)**: \[ P(10, 3) = 10 \times 9 \times 8 \] 5. **Calculate the product**: \[ 10 \times 9 = 90 \] \[ 90 \times 8 = 720 \] ### Final Answers: - \( P(8, 2) = 56 \) - \( P(10, 3) = 720 \)
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