A 6-digit security code is made using digits from O to 9. The first and the last digits are known. If the remaining four digits are known to be primes, at the most how many trials are required to determine the code?

Correct option is C

Given:

• A 6-digit security code made using digits from 0 to 9
• The first and last digits are fixed (known)
• The remaining 4 digits are primes
• We are to find the maximum number of trials required to determine the code
  (i.e., all possible combinations for the 4 unknown digits)

Solution:

• We're fixing positions: _ (known) X X X X _ (known)
• Digits can be repeated unless otherwise mentioned (assume repetitions allowed)

Step 1: Prime digits from 0–9

Digits from 0 to 9: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Prime digits = 2, 3, 5, 7 → total 4 choices for each of the 4 middle digits

Step 2: Number of possible combinations

Each of the 4 middle positions can be any of the 4 prime digits.

So total combinations =
4 × 4 × 4 × 4 = 4⁴ = 256

Correct Option: (C) 256