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Question

The characters in the phrase "THE END" are randomly rearranged. (This includes the six letters and the space.) What is the probability that
(i) The Es will appear together. (ii) The new phrase will also have two 3 letter words. (iii) There will be one 6 letter word.  [4 MARKS]


Solution

Concept : 1 Mark
Sub-parts : 1 Mark each
(i) There are 7 x 62 = 21 combinations for the positions of the 2 Es. Out of these, 6 are favourable:
EE-----
-EE----
--EE---
---EE--
----EE-
-----EE
Therefore, the required probability is 621 = 27.
(ii) For the new phrase to have 2 three letter words, the space should appear in the 4th position. Since this is one favourable outcome from seven possible outcomes, the probability is 17.
(iii) For there to be a six letter word, the space should come in the first or last position. Since this is two favourable outcomes from seven possible outcomes, the probability is 27.

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