Multiple choice

In how many ways can the letters of the word UNIVERSAL be arranged? In how many of these will E, R, S always occur together?

  1. 30240

  2. 40240

  3. 20240

  4. 60240
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A Correct answer
AI explanation

To find the arrangements where E, R, and S always occur together, we treat these three letters as a single combined block. This leaves us with 7 distinct items to arrange (the ERS block, U, N, I, V, A, L), which can be done in 7! = 5040 ways. The letters within the ERS block can be arranged among themselves in 3! = 6 ways, so multiplying these gives 5040 * 6 = 30240 total arrangements.

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