Find the number of different ways that the 9 letters of the word AGGREGATE can b

Question

Find the number of different ways that the 9 letters of the word AGGREGATE can be arranged in a line if the first letter is R. (ii) Find the number of different ways that the 9 letters of the word AGGREGATE can be arranged in a line if the 3 letters G are together, both letters A are together and both letters E are together. (iii) The letters G, R and T are consonants and the letters A and E are vowels. Find the number of different ways that the 9 letters of the word AGGREGATE can be arranged in a line if consonants and vowels occur alternatively. (iv) Find the number of different selections of 4 letters of the word AGGREGATE which contains exactly 2 Gs or exactly 3 Gs.

Explanation / Answer

1) total number of words are 9

since the first place is fixed with R

there are 3 G's , 2 A's and 2 E's

so number of ways would be

8! / 3! 2! 2!

on solving we get

= 1680 ways

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