Multiple choice

A card consists of 6 letters which can be spelled as INDORE. From this information, answer the following questions. 1. How many different words can be formed with letters of the word INDORE? 2. How many of these begin with 'I' and end with 'E'? 3. In how many of these are I and E together?

  1. 720, 24, 240

  2. 800, 24, 240

  3. 720, 25, 250

  4. 720, 24, 250

  5. 800, 34, 250
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A Correct answer
AI explanation

The word INDORE has 6 distinct letters, so the total number of words formed is 6! = 720. To begin with I and end with E, the remaining 4 distinct letters can be arranged in 4! = 24 ways. If I and E are together, we treat them as a single unit, which can be arranged internally in 2! ways; this unit and the other 4 letters give 5 entities to arrange, yielding 2! times 4! times 2 = 240 ways. The values are 720, 24, and 240.

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