SOLUTION: The number of ways a class of n student can elect a president, a vice president, a secretary, and a treasurer is given by the function P(n) = n^4 – 6n^3 + 11n^2 – 6n, where n >= 4.
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Question 261024: The number of ways a class of n student can elect a president, a vice president, a secretary, and a treasurer is given by the function P(n) = n^4 – 6n^3 + 11n^2 – 6n, where n >= 4. Use the Remainder Theorem to determine the number of ways the class can elect officers if the class consists of
(a) n = 12 students
(b) n = 24 students
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The number of ways a class of n student can elect a president, a vice president, a secretary, and a treasurer is given by the function
P(n) = n^4 – 6n^3 + 11n^2 – 6n, where n >= 4.
Use the Remainder Theorem to determine the number of ways the class can elect officers if the class consists of
(a) n = 12 students
Divide P(n) by n-12 and find the Remainder which is P(12)
12)....1....-6....11....-6....0
.........1.....6....83....990..|..11880
P(12) = 11880
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(b) n = 24 students
24)....1....-6....11....-6....0
........1.....18....443..10626..|..255024
P(24) = 255,024
=============================================
Cheers,
Stan H.
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