JEE Main 2020MathematicsPermutation CombinationMediumNumerical

JEE Main 2020 — Permutation Combination Question with Solution

JEE Main 2020 (05 Sep Shift 1)

Question

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

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Show full solutionCorrect answer: 240
Correct answer
240

Step-by-step explanation

From the given word, S-2,L-2,A,B,Y,U.

Number of alike letter pairs =2

Number of ways to select one pair=C12

Number of distinct letters=5

Number of ways to select two distinct letters=C25

Number of ways to arrange four letters if two are alike=4!2!

Required number of ways =C12C25·4!2!=2·10·242=240

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About this question

This is a previous-year question from JEE Main 2020, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.