How many different ways can the letters in the word "CORPORATION" be arranged so that the vowels always meet?
A. 810
B. 1440
C. 2880
D. 50400
Answer:D
How many different ways can the letters in the word "CORPORATION" be arranged so that the vowels always meet?
A. 810 B. 1440 C. 2880 D. 50400
Explanation: The vowels OOAIO are treated as one letter in the word 'CORPORATION.'As a result, we have CRPRTN (OOAIO).This has seven letters (six plus one), with R appearing twice and the rest being unique.The number of different ways to arrange these letters is 7!/2! = 2520.Now, 5 vowels may be arranged, with O appearing three times and the others being differen in 5!/3! = 20 different ways.The required number of ways is 50400 (2520 x 20).