JEE PYQ: Permutation And Combination Question 20
Question 20 - 2020 (05 Sep Shift 1)
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 ______.
Show Answer
Answer: 240
Solution
SYLLABUS: S(2), L(2), A, B, U, Y. Choose the repeated letter: ${}^2C_1 = 2$ (S or L). Choose 2 distinct from remaining 5: ${}^5C_2$. Arrange: $\frac{4!}{2!} = 12$. Total $= 2 \times {}^5C_2 \times 12 = 2 \times 10 \times 12 = 240$.
BETA
