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Permutation: n Different Things Taken All at a Time When All Are Not Different.

How many word...

Question

How many words can be formed with the letters of the word PATALIPUTRA without changing the relative order of vowels and consonants?

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Solution

$11$ Letters, $5 V (3 A, 1 I, 1 U), 6 C (2 P, 2 T, 1 L, 1 R)$
$∴$ Total number $= \frac{5!}{3!} \times \frac{6!}{2! 2!} = 20 \times 180 = 3600$ .

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Permutation: n Different Things Taken All at a Time When All Are Not Different.

Standard XII Mathematics

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