Permutations & Combinations
Arrangements with All Vowels Together
nta_pyq_2023_apr
Grade 11

Question:

Number of arrangements of INDEPENDENCE with all vowels always together is
16800
33600
18000
14800

Step-by-Step Solution

Key Concept: INDEPENDENCE: consonants N,D,P,N,D,N,C (7) and vowels I,E,E,E (4). Treat vowels as block. Arrange 8 units: $\frac{8!}{3!2!}\times\frac{4!}{3!}$.
16800 arrangements.
Correct Answer: 1

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