JEE PYQ: Permutation And Combination Question 28
Question 28 - 2020 (08 Jan Shift 2)
The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word ‘EXAMINATION’ is ______.
Show Answer
Answer: 2454
Solution
EXAMINATION: E, X, A(2), M, I(2), N(2), T, O. 8 distinct letters, 3 pairs (A, I, N). Case I: All different: ${}^8P_4 = 8 \times 7 \times 6 \times 5 = 1680$. Case II: Two same, two different: ${}^3C_1 \times {}^7C_2 \times \frac{4!}{2!} = 3 \times 21 \times 12 = 756$. Case III: Two pairs same: ${}^3C_2 \times \frac{4!}{2!2!} = 3 \times 6 = 18$. Total $= 1680 + 756 + 18 = 2454$.
BETA
