Permutations and Combinations

The number of 4-digit numbers formed by using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the product of the digits is 0 is ______.

The number of ways to arrange the letters of the word 'EQUATION' such that all vowels come together is ______.

The number of ways to choose 4 cards from a pack of 52 playing cards such that all four cards are of the same suit is ______.

The number of ways to choose 3 men and 2 women from a group of 7 men and 5 women is ______.

The number of ways to distribute 10 identical items among 3 distinct persons such that each person gets at least one item is ______.

The number of ways to choose 5 balls from a bag containing 6 red balls and 4 blue balls such that at least 3 red balls are chosen is ______.

The number of ways to seat 5 men and 5 women in a row such that no two women sit together is ______.

The number of ways to arrange 7 books on a shelf such that two particular books are always together is ______.

The number of ways to form a committee of 3 members from 6 men and 4 women such that the committee has at least one woman is ______.

The number of distinct permutations of the letters of the word 'MISSISSIPPI' is ______.

The number of ways to choose 2 distinct numbers from the set {1, 2, 3, ..., 10} such that their sum is even is ______.

The number of ways to arrange 3 boys and 3 girls in a row such that no two boys sit together is ______.

The number of ways to choose 4 items from a set of 10 distinct items is ______.

The number of ways to form a 3-digit number using the digits 1, 2, 3, 4, 5 without repetition is ______.

The number of ways to arrange 4 distinct objects in a circle is ______.

The number of ways to choose 3 students from a class of 10 students for a competition is ______.

The number of ways to arrange the letters of the word 'APPLE' is ______.

The number of ways to choose 2 boys and 2 girls from a group of 4 boys and 3 girls is ______.

The number of ways to distribute 5 identical balls into 3 distinct boxes is ______.

The number of ways to choose a committee of 5 members from 10 people such that a particular person is always included is ______.

The number of ways to choose a committee of 5 members from 10 people such that a particular person is always excluded is ______.

The number of ways to arrange 6 distinct books on a shelf is ______.

The number of ways to choose 3 items from a set of 7 distinct items is ______.

The number of ways to form a 4-letter word using the letters of the word 'ROSE' without repetition is ______.

The number of ways to arrange 5 distinct objects in a row is ______.

Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which P, Q and T...