Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85^th string?

Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4 and 5 repetitions not allowed?

Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?

Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three on the other side. Determine the number of ways in which the seating arrangement can be made?

If p(h) is the statement "n² + n is even" and if p(r) is true, then p(r + 1) is true.

If p(n) is the statement "n² - n + 41 is prime". Prove that p(1), p(2), and p(3) are true. Prove also that p(41) is not true.

How many 'letter strings' together can be formed with the letters of the word "VOWELS" so that
(i) the strings begin with E
(ii) the strings begin with E and end with W.

How many different strings can be formed together using the letters of the word "EQUATION" so that
(i) the vowels always come together?
(ii) the vowels never come together?

If the letter of the word 'RACHIT' are arranged in all possible ways as listed in dictionary, then what is the rank of the word 'RACHIT'?

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7 if no digit is repeated?