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If \(^6\mathrm{P}_r = 6,\) find the value of \(^6\mathrm{P}_{r + 1}\)


Question

If \(^6\mathrm{P}_r = 6,\) find the value of \(^6\mathrm{P}_{r + 1}\)

Options

A) \(30\)

B) \(33\)

C) \(35\)

D) \(15\)

Explanation:

\(^6\mathrm{P}_r = 6\) Thus \(r = 1\)
N.B: \(^6\mathrm{P}_1 = \frac{6!}{(6 - 1)!}\)
\(= \frac{6!}{5!}\) \(= \frac{6 \times 5!}{5!} = 6\)
\(^6\mathrm{P}_{r + 1} = ^6\mathrm{P}_2\) \(= \frac{6!}{(6 - 2)!} = \frac{6!}{4!}\)
\(= \frac{6 \times 5 \times 4!}{4!} = 30\)


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Dicussion (1)

  • \(^6\mathrm{P}_r = 6\) Thus \(r = 1\)
    N.B: \(^6\mathrm{P}_1 = \frac{6!}{(6 - 1)!}\)
    \(= \frac{6!}{5!}\) \(= \frac{6 \times 5!}{5!} = 6\)
    \(^6\mathrm{P}_{r + 1} = ^6\mathrm{P}_2\) \(= \frac{6!}{(6 - 2)!} = \frac{6!}{4!}\)
    \(= \frac{6 \times 5 \times 4!}{4!} = 30\)

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