Permutations and Combinations jee mains questions | JEE Main Maths Permutations and Combinations Previous Year Question

Q 11 :
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 _______. [2024]

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(3734)

The word 'DISTRIBUTION' has total 12 letters and 9 diferent letters.

We select four different letters.

Case l : Three same letters and 1 different letter ${}^{1}{C_{1}} \times {}^{8}{C_{1}} \times \frac{4!}{3!}$

Case 2 :Two pairs are same and two pairs are different ${}^{2}{C_{1}} \times {}^{8}{C_{2}} \times \frac{4!}{2!}$

Case 3 : Two pair of letters are same ${}^{2}{C_{2}} \cdot {}^{4}{C_{2}}$

Case 4 : All different letters are select ${}^{9}{C_{4}} \times 4!$

Total letters selected.

$= {}^{1}{C_{1}} \times {}^{8}{C_{1}} \times \frac{4!}{3!} + {}^{2}{C_{1}} \times {}^{8}{C_{2}} \cdot \frac{4!}{2!} + {}^{2}{C_{2}} \cdot {}^{4}{C_{2}} + {}^{9}{C_{4}} \cdot 4!$

$= 1 \times \frac{8!}{7!} \times \frac{4!}{3!} + 2! \times \frac{8!}{6! 2!} \times \frac{4!}{2!} + \frac{1 \times 4!}{2! 2!} + \frac{9! \times 4!}{5! 4!}$

$= 32 + 672 + 6 + 3024 = 3734$

Topic Question Set

Q 11 :
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 _______. [2024]

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Topic Question Set

Q 11 : 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 _______. [2024]

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Q 11 :
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 _______. [2024]