In-text Questions — Counting Passwords — Power Play

1. 12 marksGanita Prakash Cl-8 Part 1, password/lock activity in §2.3

   How many 5-digit passwords are possible, if each digit can be any of 0-9?

   Hint. Build up from the 2-digit and 3-digit cases already worked out (100 and 1000) by adding one more independent digit at a time.

   Step 1 — Recall the pattern from smaller cases. A 2-digit lock has 10 × 10 = 100 passwords; a 3-digit lock has 100 × 10 = 1000.

   Step 2 — Extend to 5 digits. Each additional digit multiplies the count by another 10, so a 5-digit lock has 10 × 10 × 10 × 10 × 10 = 10⁵.

   Step 3 — Evaluate. 10⁵ = 1,00,000.

   ✦ Answer: 1,00,000 passwords.

   Where students slip. Assuming the digits can't repeat — this lock allows any digit 0-9 in any position, including repeats, which is exactly why each position independently contributes a factor of 10.

2. 22 marksGanita Prakash Cl-8 Part 1, password/lock activity in §2.3

   Estu buys a lock with 6 slots, each showing a letter from A to Z. How many passwords are possible with such a lock?

   Hint. There are 26 letters available for each of the 6 independent slots.

   Step 1 — Count the choices per slot. Each of the 6 slots can independently be any of 26 letters.

   Step 2 — Multiply across all 6 slots. 26 × 26 × 26 × 26 × 26 × 26 = 26⁶.

   ✦ Answer: 26⁶ passwords.

   Where students slip. Adding 26 six times (26 × 6) instead of multiplying — each slot's choice is independent of the others, so the counts multiply, not add.

Solutions written by the tuition.in editorial team and checked against the NCERT Class 8 Mathematics textbook Ganita Prakash Part 1, Reprint 2026-27 (hegp102.pdf). Questions are scattered as 'Math Talk'/'Try This' prompts through the running text, plus two formal 'Figure it Out' blocks. Every answer here is checked against the book's own printed answer key at the end of the chapter.. Questions are referenced from the NCERT textbook for identification.