Words of length 10 are formed by using the letters A, B, C, D, E, F, G, H, I, J. Let x . be number of such words where no letter is repeated and y be number of such words where exactly two letters are repeated twice and no other letter is repeated, then the value of y x is

Step-by-step solution

aligned & Letters are A, B, C, D, E, F, G, H, I, J & Number of words that can be formed by & 10 letters =10! ¹⁰ C ₁₀ & x=10! aligned Now, for repetition of two letters. Two letters can be selected in ¹⁰ C ₂ ways which are used twice in the word and remaining 6 letters can be selected from 8 letters in ^8 C ₆ ways. Hence, Number of words can be formed aligned & = ¹⁰ C ₂ ^8 C ₆ 10! 2! 2! y & = ¹⁰ C ₂ ^8 C ₆ 10! 2! 2! y x & = ¹⁰ C ₂ ^8 C ₂ 10! 2! 2! 10! & = ¹⁰ C ₂ ^8 C ₆ 2! 2! & = 45 28 4 & =315 aligned