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JEE 2023 Mathematics PYQ — The number of arrangements of the letters of the word “INDE… | Mathem Solvex | Mathem Solvex

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

The number of arrangements of the letters of the word “INDEPENDENCE” in which all the vowels always occur together is.

Choose the correct answer:

A.
16800
(Correct Answer)
B.
14800
C.
18000
D.
33600

Correct Answer:

16800

Explanation

In the given word, vowels are: I, E, E, E, E Consonants are: N, D, P, N, D, N, C

\text{So, number of words} = \frac{8!}{3!2!} \times \frac{5!}{4!}

= \frac{8 \times 7 \times 6 \times 5 \times 4}{2} \times 5 = 16800

Explanation

In the given word, vowels are: I, E, E, E, E Consonants are: N, D, P, N, D, N, C

\text{So, number of words} = \frac{8!}{3!2!} \times \frac{5!}{4!}

= \frac{8 \times 7 \times 6 \times 5 \times 4}{2} \times 5 = 16800

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