JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Permutations and Combinations

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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 ____.

Answer: 240

Solution

In SYLLABUS the only repeated letters are S and L, each twice, while the distinct letters available are S, Y, L, A, B and U. A four-letter arrangement with one repeated pair and two different letters is built in three stages: choose the doubled letter from

{S, L}

2

ways; choose two distinct letters from the remaining five in

(2 5) = 10

ways; and arrange the four letters, two of them alike, in

\frac{4 !}{2 !} = 12

ways. The count is

2 \times 10 \times 12 = 240

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Integer answer

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