Combinatorics | Number Theory Answers

There are 27 members of a committee. What are the odds of guessing the 14 members of the committee that attended a meeting? How does one calculate the result ?

I need the answer to this equation:
? + ? - ? + ? - ? = 53
The numbers I have to use are: 51 25 23 40 & 62

Let n be an integer divisible by 9. Prove that n^7 = n mod 63

find the base of the numeral system in which 26-18=9(express your answer in base 10).

how many integers from 1 to 19999 have exactly 15 divisors ?

In how many ways can a student select any number of books from the library if there are 7 books of his interest?

Prove that the sum of any 7 consecutive non- negative integers is divisible by 7 . Is this true for any positive integers instead of 7

My games collection is 4 feat 5 and a half inches tall, with the average case being 3 quarters of an inch thick, how many games do have?

which is the smallest 6 digit number when divided by 5,6,7,8 respectively gives remainder as 3,4,5,6

How many numbers superior to 50000 can be formed using the digits 1,2,4,6,8 ?