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Oct 3, 2014

# How manydifferent waysthe letters of the word ALGEBRAcan be arranged in a row ?

In how many different ways the letters of the word ALGEBRA  can be arranged in a row if a) If the two A's are together? b) If the two A's are not together?

Raghunath Reddy

Member since Apr 11, 2014

Sol: In a word ALGEBRA  have 2 A's and 5 different letters are there. 1) Two A's will take 1 unit and 5 letters will take 5 units then total number units = 6. These can be arranged in 6! = 6x5x4x3x2x1 = 720 ways. 2) The number of arrangements in which two A's together is = 720 ways. The number of arrangements with out any restriction = 7! / 2! = 2520 ways. The required number of arrangements if two A's are not together = 2520 - 720 = 1800 ways.
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