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

Correct answer: 3734

We have III, TT, D, S, R, B, U, O, N

Number of words with selection (a, a, a, b)

\(={ }^{8} \mathrm{C}_{1} \times \frac{4 !}{3 !}=32\)

Number of words with selection (a, a, b, b)

\(=\frac{4 !}{2 ! 2 !}=6\)

Number of words with selection (a, a, b, c)

\(={ }^{2} C_{1} \times{ }^{8} C_{2} \times \frac{4 !}{2 !}=672\)

Number of words with selection (a, b, c, d)

\(={ }^{9} \mathrm{C}_{4} \times 4 !=3024\)

\(\therefore\mathrm { Total }=3024+672+6+32 =3734\)