Question

In how many different ways the letters of the word ALGEBRA can be arranged in a row if (1) the two A's are together? (2) the two A's are not together?

Answer 1

Answer:

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

right