CA Foundation · Quantitative Aptitude · Permutations and Combinations
How many distinct arrangements of the letters of the word COMMITTEE are there in which all the vowels stay together?
The answer is 2160. Treat the vowels O, I, E, E as one block, which can be internally arranged in 12 ways because the two E's are alike. The block with C, M, M, T, T gives 180 arrangements, and 180 multiplied by 12 equals 2160.
- A4320
- B2160Correct
- C1080
- D45360
Explanation
The vowels O, I, E, E form one block, which can be arranged in 4!/2! = 12 ways. The block plus C, M, M, T, T makes 6 units with M and T each repeated twice, giving 6!/(2!2!) = 180 arrangements. Total = 180 x 12 = 2160. The figure 4320 results from ignoring that the two E's are identical inside the block (24 x 180).
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