Question 1
Find the rank of the word 'FARM' in all permutations of its letters.
Question 2
Using digits 1, 2, 3, and 4, how many 4-digit numbers can be formed if repetition is allowed?
Question 3
Apply the Inclusion-Exclusion Principle to find the number of integers between 1 and 100 that are divisible by either 2 or 3.
Question 4
In how many ways can 5 persons be seated around a circular table?
Question 5
The number of ways to partition 12 students into three equal groups of 4 each is
Question 6
How many ways can the letters of the word 'JEE' be arranged?
Question 7
How many different 6-digit numbers can be formed by using the digits 1, 2, 3, 4, 5, and 6 without repetition?
Question 8
How many ways can you choose a 3 out of 5 candidates such that A is always included?
Question 9
How many ways can a team of 3 boys and 2 girls be formed from a class of 50 boys and 30 girls?
Question 10
Find the largest exponent of 7 in 50! (50 factorial).
Question 11
What is the number of permutations of the word 'COMPUTER' such that vowels come together?
Question 12
How many ways can 4 boys and 3 girls be seated in a row so that no two girls are adjacent?
Question 13
In how many ways can you form a committee of 4 people out of 10 men and 5 women such that there are at least 2 women?
Question 14
What is the exponent of 5 in 100! (100 factorial)?
Question 15
Determine the number of distinct permutations of the letters in the word 'MISSISSIPPI'.