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Question
Solve the following:
In how many ways can the letters of the word ARRANGEMENTS be arranged? Find the chance that an arrangement chosen at random begins with the letters EE.
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Solution
The word ‘ARRANGEMENTS’ has 12 letters in which 2A, 2E, 2N, 2R, G, M, T, S are there.
n(S) = Total number of arrangements
= `(12!)/(2! 2! 2! 2!)`
= `(12!)/(2!)^4`
A: Arrangement chosen at random begins with the letters EE.
If the first and second places are filled with EE, there are 10 letters left in which 2A, 2N, 2R, G, M, T, S are there.
∴ n(A) = `(10!)/(2!2!2!)`
= `(10!)/(2!)^3`
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(10!)/(2!)^3 xx (2!)^4/(12!)`
= `2/(12 xx 11)`
= `1/66`
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