Multiple choice

In the word "EXPERIMENT," how many different words, not essentially meaningful, can be formed using all letters, if each word must begin with the letter "T"?

  1. 60,448

  2. 60,480

  3. 60,840

  4. 64,840
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The word EXPERIMENT has 10 letters: E(3), X(1), P(1), R(1), I(1), M(1), N(1), T(1). Fixing T at the start, we arrange the remaining 9 letters (E, X, P, E, R, I, M, E, N). The number of arrangements is 9! / 3! = 362880 / 6 = 60480.

AI explanation

The word EXPERIMENT has 10 letters with E repeated 3 times. Fixing T at the first position leaves 9 positions to be filled by the remaining letters. Using the formula for arranging n items with p identical items, the number of arrangements is 9! divided by 3!, which is 362880 divided by 6. The total number of words that can be formed is 60480.

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