The total number of words (with or without meaning) that can be formed out of the letters of the word "DISTRIBUTION" taken four at a time, is equal to ______.

Step-by-step solution

Given, Word ' DISTRIBUTION ' Now, we have III , TT , D , S , R , B , U , O , N Number of words with 3 alike letter and 1 different will be, = 8 C 1 × 4 ! 3 ! = 32 Number of words with 2 alike and other 2 alike will be, = 4 ! 2 ! 2 ! = 6 Number of words with 2 alike and 2 different will be, = 2 C 1 × 8 C 2 × 4 ! 2 ! = 672 Number of words with all different letters will be, = 9 C 4 × 4 ! = 3024 Therefore, the total number of ways will be, = 3024 + 672 + 6 + 32 = 3734