## Permutations and Combinations: IITJEE Mains problem solving practice

**Problem 1:**

Find all natural numbers n such that ends with exactly 26 zeros.

**Problem 2:**

Find the largest two digit prime that divides .

**Problem 3:**

Find all natural numbers such that is divisible by 25.

**Problem 4:**

When is computed, it ends in 7 zeros. Find the digit that immediately precedes these zeros.

**Problem 5:**

Prove that is a natural number for all .

Cheers,

Nalin Pihwa.

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