# 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

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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