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.

This entry was written by Nalin Pithwa, posted on October 26, 2017 at 2:33 am, filed under combinatorics or permutations and combinations. Bookmark the permalink. Follow any comments here with the RSS feed for this post. Post a comment or leave a trackback: Trackback URL.

Leave a Reply Cancel reply

Enter your comment here...

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

Email (required) (Address never made public)

Name (required)

Website

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

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

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

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

Cancel

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this:

Mathematics Hothouse