Permutation Combination Question 7
Question 7 - 2024 (31 Jan Shift 1)
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
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Answer (3764)
Solution
We have III, TT, D, S, R, B, U, O, N
Number of words with selection ( $a, a, a, b)$
$={ }^{8} C _1 \times \frac{4 !}{3 !}=32$
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)
$={ }^{9} C _4 \times 4 !=3024$
$\therefore$ total $=3024+672+6+32$
$=3734$
