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i=1
2 3 (n+1) −(n+ 1)
3 n 2−n
+(3 ( n+1 ) −2)=
2
2 2 3n^2 – n / 2 + (3n+1) = 3 n +5 n+ 2
2 8. (10 pts) Use the permutation formula to calculate the number
permutations of
the set {V, W, X, Y, Z} taken three at a time. Also list these
permutations. 5P3 = 5!
5!
= =60
( 5−3 ) ! 2! permutations {V,W,X} {V,W,Y} {V,W,Z} {V,X,W}
{V,X,Y} {V,X,Z} {V,Y,W} {V,Y,X} {V,Y,Z} {V,Z,W} {V,Z,X}
{V,Z,Y} {W,V,X} {W,V,Y} {W,V,Z} {W,X,V} {W,X,Y} {W,X,Z}
{W,Y,V} {W,Y,X} {W,Y,Z}
{W,Z,V} {W,Z,X} {W,Z,Y} {X,V,W} {X,V,Y} {X,V,Z} {X,W,V}
{X,W,Y} {X,W,Z} {X,Y,V}
{X,Y,W} {X,Y,Z} {X,Z,V} {X,Z,W} {X,Z,Y} {Y,V,W} {Y,V,X}
{Y,V,Z} {Y,W,V} {Y,W,X} {Y,W,Z}
{Y,X,V} {Y,X,W} {Y,X,Z} {Y,Z,V} {Y,Z,W} {Y,Z,X} {Z,V,W}
{Z,V,X} {Z,V,Y} {Z,W,V} {Z,W,X}
{Z,W,Y} {Z,X,V} {Z,X,W} {Z,X,Y} {Z,Y,V} {Z,Y,W} {Z,Y,X} 9.
(10 pts) Translate the following English sentences into statements of
predicate