Combinatorics | Number Theory Answers

Let A={0,1,2,3,4,5,6,7,8,9,10}.Show that If S is any subset of A with 7 elements,then there are 2 elements of S whose sum is 10?

How many permutations of letters of the word 'MADHUBANI' do not begin with M but end with I ?

a news paper has 4 pages missing i can tell you that pages 6 and 19 are missing.
how many pages were in the original news paper?

Identify the number that is equal to five times the sum of the digits.

Six students form a friendship club. Everytime they meet they shake hands with one another. How many times do they shake hands at one meeting?

What is the number of permutations of the letters of the word HINDUSTAN such that neither the pattern
"HIN" nor "DUS" nor "TAN" appears ?

"Insert 3 rational numbers between -5 and -4" this is my problem pls solve it.

Timothy is conducting an experiment where he flips a two-sided coin 5 times. How many different outcomes could Timothy's experiment have?

My question is what are some different things you can do to a number/numbers? (add, subtract, multiply divide, multiply by itself find the opposite)
How can you find more ways to do things with numbers?

what is the probability to get rain exactly 4 days during a week if probability to get rain in a randomly selected day p 0.4