leeto wrote:
How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word GREGARIOUS ?
A) \(_8P_2\)
B) \(\frac{_8P_2}{2!2!}\)
C) \(_8P_4\)
D) \(\frac{_8P_4}{2!2!}\)
E) \(\frac{_{10}P_2}{2!2!}\)
Could you confirm that my answer is indeed correct ? Many thx in advance.
Responding to a pm:
2G, 2R, A, E, I, O, U, S
You will need to make cases - the 3 different ways in which you can make 4 letter words:
Case 1: 2 Same, 2 Same - Pick G and R and arrange them as 4!/2!*2!
Case 2: 2 Same, 2 Different - Pick one of G and R in 2 ways. Of the remaining 7 distinct letters, pick any 2 in 7C2 ways. Arrange them in 4!/2! ways
Case 3: All 4 different - Out of 8 distinct letters, pick any 4 in 8C4 ways. Arrange them in 4! ways.
Total number of ways = 4!/2!*2! + 2 * 7C2 * 4!/2! + 8C4 * 4!
_________________
Karishma
Veritas Prep GMAT Instructor
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