Combinatorics | Number Theory Answers

7×TUSHER=6×HERTUS
every alphabet here will be a number
For Further information:
T/U/S/H/E/R=0,1,2,3,4,5,6,7,8,9

SOLVE THE EQUATION ABOVE.

In how many ways can a class of 22 students be split into two groups of 9 and 13 respectively if there is a pair of twins who must not be separated? (4 Marks)

Ques.1
5 girls and 5 boys are to be seated around a circular table such that no 2 girls will sit together the number of ways in which they can be seated around the table is?
Ques2: 6 women and 5 men are to be seated in a row so that no two men can sit together number of ways they can be seated is?
What is circular permulation and why we do (n-1) and (n-1)/2

At least how many 8's are needed after 1 to make a number which can be expressed as x^64, where x is an integer?

1. A = {1,2,3,...,2016,2017,2018} S is a set whose elements are the subsets
of A such that one element of S cannot be a subset of another element. Let, S has
maximum possible number of elements. In this case, what is the number of
elements of S?

How many ways are there to arrange the letters in the word Garden with the vowels in alphabetical order?

Number greater than or equal to 1000 but less than or equal to 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed) is....

1. How many of first 100 terms in the sequence 3, 5, 7, 9, 11, 13, 15...... are
divisible by 6?
2. 26th March is the Independence Day of Bangladesh. Independence of
Bangladesh was declared on 26/03/1971. Find out the largest number that can be
formed by taking multiplication of any two out of all the prime factors of the
product of 26, 03 and 2010.

1. Let S= 1^1 + 2^2+3^3+.....+2010^2010. . What is the remainder when S is divided by 2?
2. Find the number of odd coefficients in expansion of (x + y)^2010.
3. Find all prime numbers p and integers a and b (not necessarily positive) such that p^a + p^b
is the square of a rational number.

Prove that every composite number in Z is reducable