Permutations and Combinations: IITJEE Mains problem solving practice

Problem 1:

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

Problem 2:

Find the largest two digit prime that divides 200 \choose 100.

Problem 3:

Find all natural numbers n \leq 14 such that n! + (n+1)!+(n+2)! is divisible by 25.

Problem 4:

When 30! is computed, it ends in 7 zeros. Find the digit that immediately precedes these zeros.

Problem 5:

Prove that \frac{(n^{2})!}{((n)!)^{n+1}} is a natural number for all n \in N.

Cheers,

Nalin Pihwa.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: