If 6Pr = 6, find the value of 6Pr+1
The correct answer is A. 30
The formula for permutations is \(^{n}P_{r} = \frac{n!}{(n-r)!}\) Given that \(^{6}P_{r} = 6\), we can solve for r:
\(6 = \frac{6!}{(6-r)!}\)
\(6(6-r)! = 6!\)
\((6-r)! = \frac{6!}{6}\)
\((6-r)! = 5!\)
\((6-r) = 5\)
\(r = 1\)
Now that we know the value of r, we can find the value of \(^{6}P_{r+1}\):
\(^{6}P_{r+1} = ^{6}P_{2} = \frac{6!}{(6-2)!} = \frac{720}{24} = 30\)
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