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 \_\_\_\_\_\_\_\_\_\_.
Answer: 3734
Solutions · 1
Official solution
DISTRIBUTION has letters: D,I,S,T,R,I,B,U,T,I,O,N --- with I\times 3, T\times 2, and D,S,R,B,U,O,N once each (9 distinct letters total, with I and T repeating).
All 4 distinct: choose 4 from the 9 distinct letters and arrange: 9P4=9×8×7×6=3024
One letter repeated twice (T, since I could give 3 but this case is exactly 2), other 2 distinct from remaining 8: for repeated letter = T: (28)×2!4!=28×12=336; for repeated letter = I (using 2 of its 3 copies): similarly 336
One letter repeated three times (I): other 1 distinct from remaining 8: (18)×3!4!=8×4=32
Two letters each repeated twice (I and T): 2!2!4!=6
\[\text{Total} = 3024+336+336+32+6 = 3734\]