StatstriveISI intelligencePractice
Back to MSQE practice
PEAMCQEasy

2022 PEA Q15

Number of arrangements of the word ``PANDEMIC'' (8 distinct letters) such that the vowels appear together.

Reveal answer and solution

Answer

A

Solution

  1. 1

    The word PANDEMIC has 88 distinct letters with three vowels (A, E, I) and five consonants

  2. 2

    (P, N, D, M, C). Treat the vowel block as a single super-letter together with the 55 consonants:

  3. 3

    66 units in total, arranged in 6!6! ways. The vowels inside the block can be permuted in 3!3! ways.

  4. 4

    Total =6!⋅3!=6⋅5!⋅3!=6×(3!)(5!)= 6! \cdot 3! = 6 \cdot 5! \cdot 3! = 6 \times (3!)(5!).

Answer structure / marking notes

6!=6⋅5!6! = 6 \cdot 5!, so the factor in front of (3!)(5!)(3!)(5!) is 66, not 55.

Content note

Imported from public/resources/isi/msqe/solutions/pea/2022/ISI_MSQE_PEA_2022_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.