StatstriveISI intelligencePractice
Back to MSQE practice
PEAMCQEasy

2024 PEA Q13

What is the number of possible arrangements of the letters of the word madam' such that the two a's never appear in consecutive positions?

Reveal answer and solution

Answer

C

Solution

  1. 1

    Letters: m,a,d,a,mm,a,d,a,m. Total distinct arrangements =5!2! 2!=30=\dfrac{5!}{2!\,2!}=30.

  2. 2

    Arrangements with both aa's together: treat `aa' as a single block, leaving symbols {m,d,m,aa}\{m,d,m,aa\}, total 4!2!=12\dfrac{4!}{2!}=12.

  3. 3

    Arrangements where the two aa's are not consecutive =30−12=18=30-12=18.

Answer structure / marking notes

Account for the repeated mm's when counting both the full and the `aa-together' arrangements.

%=========================================================

Content note

Imported from public/resources/isi/msqe/solutions/pea/2024/ISI_MSQE_PEA_2024_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.