The position of how many letters will change, if each of the letters in the word ‘SYSTEM’ is arranged in the English alphabetical order?

Correct — B. Rule: stack the alphabetised string under the original and count the columns that differ.

SYSTEM sorted into English alphabetical order is EMSSTY.

Position 1: S → E, changed.
Position 2: Y → M, changed.
Position 3: S → S, unchanged.

Position 4: T → S, changed.
Position 5: E → T, changed.
Position 6: M → Y, changed.

Only position 3 holds, so five positions change.

Why the others are wrong

• (a)
  Three — Three badly under-counts. Stack EMSSTY under SYSTEM and five of the six columns show different letters.
• (c)
  Four — Four is what you get if you decide a second position also holds, usually by losing track of which S is which. There is exactly one unchanged column, position 3.
• (d)
  Six — Six assumes nothing survives the sort, but position 3 carries S before and S after, so that one column does not change.

The question compares two strings made of the same six letters — the word and its alphabetised form — and counts the positions where the letter differs.

The reliable method is mechanical: sort, write the sorted string directly under the original, run down the columns.

Repeated letters are the only real complication. SYSTEM has two S's, and in EMSSTY they sit at positions 3 and 4. Position 3 already held an S, so that column is unchanged and the count comes to five, not six.

Key facts

• SYSTEM alphabetised is EMSSTY.
• A position is judged by the letter standing there, so a repeated letter can leave a position unchanged.
• Only position 3 holds here, so five positions change.

Common traps

• Answering six on the assumption that a full sort must disturb everything
• Losing track of the two S's and reporting four
• Sorting correctly but comparing by eye instead of stacking the two strings

No directly related past PYQ was found.