Solve for n.? $56 ^ { . }~ {}_{ n - 1} P _ { 6 } = { } _ { n + 1 } P _ { 7 }$
A)no solution
B)?n = 7
C)?n = 7,48
D)?n = 8,47
E)?n = 48

Question

Quizplus · Accepted Answer

The equation involves permutations, which are defined as $_n P_r = \frac{n!}{(n-r)!}$. Given $56 ^ { . }~ {}_{ n - 1} P _ { 6 } = { } _ { n + 1 } P _ { 7 }$, we can express both sides in terms of factorials: $\frac{(n-1)!}{(n-7)!} = \frac{(n+1)!}{(n-6)!}$. Simplifying both sides by canceling out common terms and solving for $n$ yields two solutions: $n = 7$ and $n = 48$.

Solve for N 56. n−1P6=n+1P756 ^ { . }~ {}_{ n - 1} P _ { 6 } = { } _ { n + 1 } P _ { 7 }56. n−1​P6​=n+1​P7​

Solve for N $56 ^ { . }~ {}_{ n - 1} P _ { 6 } = { } _ { n + 1 } P _ { 7 }$