The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is ______.
Option: 1 360
Option: 2 420
Option: 3 120
Option: 4 240

Answers (1)

SYLLABUS

2S and 2L

We need to form word of the type  XYZZ

\\\text{selection of 2 alike letters }=^2C_1\\\text{selection of 2 distinct letters }=^5C_2

Total number of ways

^2C_1\times^5C_2\times\frac{4!}{2!}=240

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