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The Delta Course GMAT Practice Questions Daily Quantitative E-mail
SOLUTION How many different distinct ways can the letters in the word VACATION be arranged? A. 25,375 B. 40,320 C. 52,500 D. 20,160 E. 5,040 If you are arranging n items in a set, the number of different permutations possible is n!. n! is pronounced n factorial. n! = n(n-1)(n-2)(n-3) . . . * 2 * 1 For instance, 2! = 2 * 1 3! = 3 * 2 * 1 4! = 4 * 3 * 2 * 1 Since there are 8 letters in the word vacation, the number of ways to arrange the letters is 8! or 40320. However, this problem asks for the number of different distinct ways. Since there are two letter A's in the word, the different distinct ways of arranging the two A's are indistinguishable. To find the number of distinct permutations, divide the factorial of the elements in the set by the factorial of the number of identical elements. Thus, the number of different distinct ways to arrange the letters in the word VACATION is (40320/2) or 20,160. The answer to today's Delta Course e-mail is D. Graduate Management Admissions Test and GMAT are registered trademarks of the Graduate Management Admission Council. This e-mail has no affiliation with nor is endorsed by the Graduate Management Admission Council. Copyright 2003 by The Delta Course, All Rights Reserved. |