What is the value of $^{m} P_{m - 1}$ ?

\frac{m!}{m!}

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\frac{m!}{(m - 1)!}

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m!

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None of the above

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Solution

The correct option is C $m!$
We know that $^{n} P_{r} = \frac{n!}{(n - r)!}$ .
According to question $n = m$ and $r = (m - 1)$

Putting the values in the equation we get,
$^{m} P_{m - 1} = \frac{m!}{[m - (m - 1)]!}$
$^{m} P_{m - 1} = \frac{m!}{[m - m + 1]!}$
$^{m} P_{m - 1} = \frac{m!}{1!} = m! .$

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What is the value of mPm−1?

The correct option is C m!We know that nPr=n!(n−r)!. According to question n=m and r=(m−1) Putting the values in the equation we get, mPm−1=m![m−(m−1)]! mPm−1=m![m−m+1]! mPm−1=m!1!=m!.

What is the value of $^{m} P_{m - 1}$ ?

The correct option is C $m!$
We know that $^{n} P_{r} = \frac{n!}{(n - r)!}$ .
According to question $n = m$ and $r = (m - 1)$

Putting the values in the equation we get,
$^{m} P_{m - 1} = \frac{m!}{[m - (m - 1)]!}$
$^{m} P_{m - 1} = \frac{m!}{[m - m + 1]!}$
$^{m} P_{m - 1} = \frac{m!}{1!} = m! .$