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# How many different four-letter words can be formed (the wor

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How many different four-letter words can be formed (the wor [#permalink]  14 May 2019, 00:05
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How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word GREGARIOUS such that each word starts with G and ends with R?

(A) $$8P_2$$

(B) $$\frac{8P_2}{2!*2!}$$

(C) $$8P_4$$

(D) $$\frac{8P_4}{2!*2!}$$

(E) $$\frac{10P_2}{2!*2!}$$
[Reveal] Spoiler: OA

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Re: How many different four-letter words can be formed (the wor [#permalink]  10 Feb 2020, 19:30
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Carcass wrote:
How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word GREGARIOUS such that each word starts with G and ends with R?

(A) $$8P_2$$

(B) $$\frac{8P_2}{2!*2!}$$

(C) $$8P_4$$

(D) $$\frac{8P_4}{2!*2!}$$

(E) $$\frac{10P_2}{2!*2!}$$

Place one G in the first slot and one R in the last slot:

G __ __ R

The remaining letters, {G, R, E, A, I, O, U, S}, can be arranged in the remaining 2 slots in $$8P_2$$ [no indistinguishable(same) objects nor repetition]. The answer is (A).

Note: Since the two G’s in the base word are indistinguishable, the word G 1 G 2 AR is the same as G 2 G 1 AR. Hence, the internal arrangement of the G’s or, for the same reason, the R’s is not important.
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Re: How many different four-letter words can be formed (the wor   [#permalink] 10 Feb 2020, 19:30
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# How many different four-letter words can be formed (the wor

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