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 (integer)
3734
Solution
<p>We have III, TT, D, S, R, B, U, O, N</p>
<p>Number of words with selection (a, a, a, b)</p>
<p>$={ }^8 \mathrm{C}_1 \times \frac{4 !}{3 !}=32$</p>
<p>Number of words with selection (a, a, b, b)</p>
<p>$=\frac{4 !}{2 ! 2 !}=6$</p>
<p>Number of words with selection (a, a, b, c)</p>
<p>$={ }^2 \mathrm{C}_1 \times{ }^8 \mathrm{C}_2 \times \frac{4 !}{2 !}=672$</p>
<p>Number of words with selection (a, b, c, d)</p>
<p>$$\begin{aligned}
& ={ }^9 \mathrm{C}_4 \times 4 !=3024 \\\\
& \therefore \text {Total }=3024+672+6+32 \\\\
& =3734
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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