Multiple choice

In the word 'MATHEMATICS', the positions of vowels and consonants are kept unchanged. How many different words can be formed by using different arrangements of the remaining letters?

  1. 15,120

  2. 15,130

  3. 15,200

  4. 15,210

  5. None of the above
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A Correct answer
Explanation

MATHEMATICS has 11 letters: M, A, T, H, E, M, A, T, I, C, S. Vowels: A, E, A, I (4). Consonants: M, T, H, M, T, C, S (7). Positions of vowels and consonants are fixed. We need to arrange the 7 consonants (M, T, H, M, T, C, S). Total arrangements = 7! / (2! * 2!) = 5040 / 4 = 1260. The question asks for arrangements of remaining letters, but the calculation 15120 suggests a different interpretation or error.

AI explanation

The word MATHEMATICS has 11 letters, consisting of 4 vowels and 7 consonants. Keeping the positions unchanged, the 4 vowels can be rearranged among themselves in 4! divided by 2!, which is 12 ways, since A appears twice. The 7 consonants can be rearranged in 7! divided by (2! multiplied by 2!), which equals 1260 ways, since M and T each appear twice. Multiplying these gives 12 multiplied by 1260, resulting in 15120 different words.

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