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Secrets of pascal triangle

What are sexy prime numbers?

In how many ways can 8 people be seated on a bench if 3 particular people must sit together?

from 24 to 12943 how many numbers can be made such that 1,3,5 does not appear 3 or more than 3 times

How many integers are there in between 1 and 500 divisible by 3 or 5

If n is greater than or equal to 9, and n-2 and n+2 are both primes, then 3|n.

A printer numbers the pages of a book starting with one and uses 3189 digits in all. How many pages does the book have?

How do I find the answer? let n=9+99+999+…+9999…9;where the last number consist of 1999 digits of 9.How many times will the digit 1 appear in n ?

1. Daniel chooses some distinct subsets of {1,...... ,2019 }such that any two distinct subsets chosen are

disjoint. Compute the maximum possible number of subsets he can choose.

3. Compute the smallest positive integer that can be expressed as the product of four distinct integers.

disjoint. Compute the maximum possible number of subsets he can choose.

3. Compute the smallest positive integer that can be expressed as the product of four distinct integers.

Five animals are assigned five different treatments. In how many ways can this be done.