Question

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 1

The letters in the word 'DISTRIBUTION' are: I, I, I, T, T, D, S, R, B, U, O, N.

Calculate the number of words formed using different combinations:

1. Number of words with selection (a, a, a, b): $\binom{4}{1} \times \frac{4!}{3!} = 32$
2. Number of words with selection (a, a, b, b): $\frac{4!}{2! \cdot 2!} = 6$
3. Number of words with selection (a, b, c, c): $\binom{2}{1} \times \binom{2}{1} \times \frac{4!}{2!} = 672$
4. Number of words with selection (a, b, c, d): $\binom{4}{1} \times 4! = 3024$

Total number of words:

$\text{Total} = 3024 + 672 + 6 + 32 = 3734$